Question

Subtract:$\frac{y}{y+4}-\frac{y-2}{y-5}$.

Short answer

The subtraction of the rational expression is$\frac{-7y+8}{\left(y-5\right)\left(y+4\right)}$.

Step-by-step solution

Given  information 

The given rational expression is$\frac{y}{y+4}-\frac{y-2}{y-5}$.

The simplification of the rational expression 

$\frac{y}{y+4}-\frac{y-2}{y-5}$

The LCD of the rational expression is$\left(y+4\right)\left(y-5\right)$.

Change into equivalent fraction with the LCD.

$\frac{y\left(y-5\right)}{\left(y+4\right)\left(y-5\right)}-\frac{\left(y-2\right)\left(y+4\right)}{\left(y-5\right)\left(y+4\right)}$

Simplify numerator

$\frac{y^2-5y}{\left(y+4\right)\left(y-5\right)}-\frac{y^2-2y+4y-8}{\left(y-5\right)\left(y+4\right)}$

$$\begin{gathered} \frac{y^2-5y-y^2-2y+8}{\left(y-5\right)\left(y+4\right)} \\ Simplify \\ \frac{-7y+8}{\left(y-5\right)\left(y+4\right)} \end{gathered}$$