Armorikam

2021-09-03

Simplifying a rational expression with two variables.
$\frac{{x}^{2}+xy-2{y}^{2}}{{x}^{2}+3xy+2{y}^{2}}$

Ayesha Gomez

Step 1
The given rational expression is,
$\frac{{x}^{2}+xy-2{y}^{2}}{{x}^{2}+3xy+2{y}^{2}}$
Step 2
It is simplified as follows.
$\frac{{x}^{2}+xy-2{y}^{2}}{{x}^{2}+3xy+2{y}^{2}}=\frac{{x}^{2}-xy+2xy-2{y}^{2}}{{x}^{2}+xy+2xy+2{y}^{2}}$
$=\frac{x\left(x-y\right)+2y\left(x-y\right)}{x\left(x+y\right)+2y\left(x+y\right)}$
$=\frac{\left(x+2y\right)\left(x-y\right)}{\left(x+2y\right)\left(x+y\right)}$
$=\frac{x-y}{x+y}$

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