Question

I dont understand this

Answer 1

`(1)/(2x(x-1))`

Explanation:

Given

`(x^2+2x+1)/(x^2-1)/ (2x^2+2x)`

Consider the numerator:

`x^2+2x+1=(x+1)^2`

Consider the denominator:

`x^2-1=(x-1)(x+1)`

Hence, the fraction becomes

`((x+1)^2)/((x-1)(x+1))=(x+1)/(x-1)`

Consider the expression in brackets:

`2x^2+2x=2x(x+1)`

Divide:

`(x^2+2x+1)/(x^2-1)/ (2x^2+2x)=(x+1)/(x-1)/ 2x(x+1)=(x+1)/(x-1)* (1)/(2x(x+1))=(1)/(2x(x-1))`