Question

Simplify the rational expression$\frac{x^2+4x-5}{x^2-2x+1}$

Short answer

The simplified form of rational expression$\frac{x^2+4x-5}{x^2-2x+1}is\frac{x+5}{x-1},x\ne 1.$

Step-by-step solution

Step 1. Given information 

Given rational expression is $\frac{x^2+4x-5}{x^2-2x+1}$.

we have to simplify this expression .

Step 2.  Simplification of rational expression

To simplify first we have to find the factors of both numerator and denominator and then divide out the common factors.

So the simplified form of the rational expression

$\begin{array}{rcl}\frac{x^2+4x-5}{x^2-2x+1}& =& \frac{(x+5)(x-1)}{(x-1)(x-1)}\\ & =& \frac{(x+5)}{(x-1)},x\ne 1\sin ce(x-1)isthecommonfactor.\\ & & \\ & & \\ & & \end{array}$