Question

Please help me solve this

Answer 1

-2/(2x+1)

Explanation:

You want the value of the rational function f(x) = (2x -2)/(x +3) for the argument (x-1)/(x+1).

Function evaluation

To evaluate a function with a rational function argument, we must replace the independent variable with the argument value, then simplify.

`f(x)=(2x-2)/(x+3)\\\\f \left((x-1)/(x+1)\right)=(2(x-1)/(x+1)-2)/((x-1)/(x+1)+3)\\\\\\=(2(x-1)-2(x+1))/((x-1)+3(x+1))=(2x-2-2x-2)/(x-1+3x+3)=(-4)/(4x+2)\\\\\boxed{f \left((x-1)/(x+1)\right)=-(2)/(2x+1)}\qquad\text{reduce the fraction}`