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simplify 9/10÷ 3

fractions and integers

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sqrt(3a+10) = sqrt(2a-1) + 2

sqrt(3a+10)=sqrt(2a-1)+2 To remove the radical on the left-hand side of the equation, square both sides of the equation. (~(3a+10))^(2)=(~(2a-1)+2)^(2) Simplify the left-hand side of the equation. 3a+10=(~(2a-1)+2)^(2) Squaring an expression is the same as multiplying the expression by itself 2 times. 3a+10=(~(2a-1)+2)(~(2a-1)+2) Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials.  First, multiply the first two terms in each binomial group.  Next, multiply the outer terms in each group, followed by the inner terms.  Finally, multiply the last two terms in each group. 3a+10=(~(2a-1)*~(2a-1)+~(2a-1)*2+2*~(2a-1)+2*2) Simplify the FOIL expression by multiplying and combining all like terms. 3a+10=(~(2a-1)^(2)+4~(2a-1)+4) Remove the parentheses around the expression ~(2a-1)^(2)+4~(2a-1)+4. 3a+10=~(2a-1)^(2)+4~(2a-1)+4 Raising a square root to the square power results in the expression inside the root. 3a+10=(2a-1)+4~(2a-1)+4 Add 4 to -1 to get 3. 3a+10=2a+3+4~(2a-1) Since a is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation. 2a+3+4~(2a-1)=3a+10 Move all terms not containing ~(2a-1) to the right-hand side of the equation. 4~(2a-1)=-2a-3+3a+10 Simplify the right-hand side of the equation. 4~(2a-1)=a+7 Divide each term in the equation by 4. (4~(2a-1))/(4)=(a)/(4)+(7)/(4) Simplify the left-hand side of the equation by canceling the common terms. ~(2a-1)=(a)/(4)+(7)/(4) To remove the radical on the left-hand side of the equation, square both sides of the equation. (~(2a-1))^(2)=((a)/(4)+(7)/(4))^(2) Simplify the left-hand side of the equation. 2a-1=((a)/(4)+(7)/(4))^(2) Combine the numerators of all expressions that have common denominators. 2a-1=((a+7)/(4))^(2) Expand the exponent of 2 to the inside factor (a+7). 2a-1=((a+7)^(2))/((4)^(2)) Expand the exponent 2 to 4. 2a-1=((a+7)^(2))/(4^(2)) Simplify the exponents of 4^(2). 2a-1=((a+7)^(2))/(16) Multiply each term in the equation by 16. 2a*16-1*16=((a+7)^(2))/(16)*16 Simplify the left-hand side of the equation by multiplying out all the terms. 32a-16=((a+7)^(2))/(16)*16 Simplify the right-hand side of the equation by simplifying each term. 32a-16=(a+7)^(2) Since (a+7)^(2) contains the variable to solve for, move it to the left-hand side of the equation by subtracting (a+7)^(2) from both sides. 32a-16-(a+7)^(2)=0 Squaring an expression is the same as multiplying the expression by itself 2 times. 32a-16-((a+7)(a+7))=0 Multiply -1 by each term inside the parentheses. 32a-16-a^(2)-14a-49=0 Since 32a and -14a are like terms, add -14a to 32a to get 18a. 18a-16-a^(2)-49=0 Subtract 49 from -16 to get -65. 18a-65-a^(2)=0 Move all terms not containing a to the right-hand side of the equation. -a^(2)+18a-65=0 Multiply each term in the equation by -1. a^(2)-18a+65=0 For a polynomial of the form x^(2)+bx+c, find two factors of c (65) that add up to b (-18).  In this problem -5*-13=65 and -5-13=-18, so insert -5 as the right hand term of one factor and -13 as the right-hand term of the other factor. (a-5)(a-13)=0 Set each of the factors of the left-hand side of the equation equal to 0. a-5=0_a-13=0 Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides. a=5_a-13=0 Set each of the factors of the left-hand side of the equation equal to 0. a=5_a-13=0 Since -13 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 13 to both sides. a=5_a=13 The complete solution is the set of the individual solutions. a=5,13

how to solve for x with fractions

Simplifying x3 + 3x2 + -4x = 0 Reorder the terms: -4x + 3x2 + x3 = 0 Solving -4x + 3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 3x + x2) = 0 Factor a trinomial. x((-4 + -1x)(1 + -1x)) = 0 Subproblem 1 Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0 Subproblem 2 Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4 Subproblem 3 Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1 Solution x = {0, -4, 1}

Whats 3x-2 over 9 equals 25 over 3x-2?

I will give you an example for this question. This might be able to help you. Simplifying 3x2 + 25x = 18 Reorder the terms: 25x + 3x2 = 18 Solving 25x + 3x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 25x + 3x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 25x + 3x2 = 0 Factor a trinomial. (-9 + -1x)(2 + -3x) = 0 Subproblem 1 Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9 Subproblem 2 Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667 Solution x = {-9, 0.6666666667}

(13-3)x5=50

Simplifying x + 2 = 3x + -1x2 + 5 Reorder the terms: 2 + x = 3x + -1x2 + 5 Reorder the terms: 2 + x = 5 + 3x + -1x2 Solving 2 + x = 5 + 3x + -1x2 Solving for variable 'x'. Reorder the terms: 2 + -5 + x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Combine like terms: 2 + -5 = -3 -3 + x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Combine like terms: x + -3x = -2x -3 + -2x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Reorder the terms: -3 + -2x + x2 = 5 + -5 + 3x + -3x + -1x2 + x2 Combine like terms: 5 + -5 = 0 -3 + -2x + x2 = 0 + 3x + -3x + -1x2 + x2 -3 + -2x + x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 -3 + -2x + x2 = 0 + -1x2 + x2 -3 + -2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3 + -2x + x2 = 0 Factor a trinomial. (-1 + -1x)(3 + -1x) = 0 Subproblem 1 Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1 Subproblem 2 Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3 Solution x = {-1, 3}

(8x)[(2x)^-2=8

Simplifying 8x = 2x2 + 8 Reorder the terms: 8x = 8 + 2x2 Solving 8x = 8 + 2x2 Solving for variable 'x'. Reorder the terms: -8 + 8x + -2x2 = 8 + 2x2 + -8 + -2x2 Reorder the terms: -8 + 8x + -2x2 = 8 + -8 + 2x2 + -2x2 Combine like terms: 8 + -8 = 0 -8 + 8x + -2x2 = 0 + 2x2 + -2x2 -8 + 8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + 8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 4x + -1x2) = 0 Factor a trinomial. 2((-2 + x)(2 + -1x)) = 0 Ignore the factor 2. Subproblem 1 Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2 Subproblem 2 Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2 Solution x = {2, 2}

what is the answer for x/7+4=x/7

(x)/(7)+4=(x)/(7) Multiply each term in the equation by 7. (x)/(7)*7+4*7=(x)/(7)*7 Simplify the left-hand side of the equation by canceling the common terms. x+28=(x)/(7)*7 Simplify the right-hand side of the equation by simplifying each term. x+28=x Since x contains the variable to solve for, move it to the left-hand side of the equation by subtracting x from both sides. x+28-x=0 Since x and -x are like terms, add -x to x to get 0. 0+28=0 Remove the 0 from the polynomial; adding or subtracting 0 does not change the value of the expression. 28=0 Since 28 is not equal to 0, there are no solutions. No Solution

Write out the solution to the equation : x + y - z = 0, 2x + 4y - z = 0 and 3x + 2y + 2z = 0

first equation: x + y - z = 0 x + y = z in the other 2 equations, replace z with x + y: 2x + 4y -(x+y) = 0 3x + 2y +2(x+y) = 0 simplify: 2x + 4y -x -y = 0 3x + 2y +2x +2y = 0 simplify more: x + 3y = 0 5x + 4y = 0 in the top equation, move the 3y to the other side: x = -3y in the bottom equation, replace x with -3y: 5(-3y) + 4y = 0 -15y +4y = 0 -11y = 0 y = 0 but x = -3y, so: x = -3(0) x = 0 but x + y - z = 0, so: 0 + 0 - z = 0 z = 0 Answer:  x = 0, y = 0, z = 0

find a particular solution (e^x+y +ye^y)dx+(xe^y -1)dy=0 if y(0)=-1

This has the form of an exact DE. Let's see if it is.  First rewrite: (e^x+y+ye^y)+(xe^y-1)dy/dx=0=A(x,y)+B(x,y)dy/dx=0 where A=e^x+y+ye^y and B=xe^y-1. (p.d.=partially differentiate; wrt=with respect to)   Take A and p.d. wrt y=1+ye^y+e^y (a) Take B and p.d wrt x=e^y (b) Since (a)<>(b) we don't have an exact DE. (If it had been an exact DE, the two quantities would have been equal.) Can we find an integrating factor u such that p.d. wrt y of uA = p.d. wrt x of uB? That is, can we find u for (at this point u can be a function of x or y or both): D(ue^x)/Dy+D(uy)/Dy+D(uye^y)/Dy=D(uxe^y)/Dx-Du/Dx? (D is del or p.d.) e^xDu/Dy+u+yDu/Dy+u(ye^y+e^y)+ye^yDu/Dy=ue^y+xe^yDu/Dx-Du/Dx. This simplifies a little: e^xDu/Dy+u+yDu/Dy+uye^y+ye^yDu/Dy=xe^yDu/Dx-Du/Dx. u(1+ye^y)=(xe^y-1)Du/Dx-(e^x+y+ye^y)Du/Dy. If u is stipulated to be a function of x only then Du/Dy=0 and the above simplifies further: u(1+ye^y)=(xe^y-1)Du/Dx. Similarly, if u is a function of y only then Du/Dx=0 and: u(1+ye^y)=-(e^x+y+ye^y)Du/Dy. More to follow...

simplify 6x/x+3=9/x-3-15/x^2-9

6x / (x + 3) = [9 / (x - 3)] - [15 / (x^2 - 9)] 6x(x - 3) / (x + 3)(x - 3) = [9(x + 3) / (x + 3)(x - 3)] - [15 / (x^2 - 9)] (6x^2 - 18x) / (x^2 - 9) = [(9x + 27) / (x^2 - 9)] - [15 / (x^2 - 9)] 6x^2 - 18x = 9x + 27 - 15 6x^2 - 18x - 9x - 12 = 0 6x^2 - 27x - 12 = 0 2x^2 - 9x - 4 = 0 2(x^2 - (9/2)x) - 4 = 0 2(x - (9/4))^2 - (81/8) - 4 = 0 2(x - (9/4))^2 = 113 / 8 (x - (9/4))^2 = 113 / 16 x - 9/4 = sqrt(113 / 16) or = -sqrt(113 / 16) x = 9/4 + sqrt(113 / 16) or x = 9/4 - sqrt(113 / 16)

how would you simplify this expression (1/y)+(2/7)-(3/2y^2)

(1/y) +(2/7) -(3/2y^2)=0 multipli bi y^2...y +(2/7)y^2 -(3/2)=0 or 14*(2/7)y^2 +14y -14*(3/2)=0 4y^2 +14y -21=0 or (x-1.1331406)(x+4.6331406)=0