Insert the required factor in the parentheses x 1x2 2x 22

Insert the required factor in the parentheses x + 1/(x^2 + 2x - 2)^2 = ( )1/(x^2 + 2x - 2)^2(4x + 4)

Solution

let unknown blank be y

((x+1)/(x²+2x-2)²) =(y)(1/(x²+2x-2)² )(4x+4)

multiply be (x²+2x-2)² on both sides

((x+1)/(x²+2x-2)²)(x²+2x-2)² =(y)(1/(x²+2x-2)² )(4x+4)(x²+2x-2)²)

(x+1) =(y)(4x+4)

(x+1) =(y)(4)(x+1)

divide by x+1 on both sides

(x+1)/(x+1)   =(y)(4)(x+1)/(x+1)  

1=4 y

y=1/4

required factor in parenthesis is 1/4