Question

`(2x+1)/(x+1) .( (x-1)(x+1) )/(4x^2 - 1)`

Answer 1

`(2x+1)/(x+1).((x-1)(x+1))/(4x^2-1)`

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

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

Answer 2

`(2x+1)/(x+1) .( (x-1)(x+1) )/(4x^2 - 1)`

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

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

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

Answer 3

\(\dfrac{2x+1}{x+1}.\dfrac{\left(x-1\right)\left(x+1\right)}{4x^2-1}\\ \Leftrightarrow\dfrac{\left(2x+1\right).\left(x^2-1\right)}{\left(x+1\right).\left(4x^2-1\right)}\\ \Leftrightarrow\dfrac{2x^3-2x+x^2-1}{4x^3-x+4x^2-1}\)