2022-01-15

Given the expression, $\frac{{x}^{2}-9}{{x}^{2}-5x+6}$, which of the following is completely simplified?

sukljama2

Step 1
Given,
The expression
$\frac{{x}^{2}-9}{{x}^{2}-5x+6}$
We have to simplify the expression.
Step 2
We have
$\frac{{x}^{2}-9}{{x}^{2}-5x+6}$
$⇒\frac{{x}^{2}-{3}^{2}}{{x}^{2}-3x-2x+6}$ (done factorization)
$⇒\frac{\left(x+3\right)\left(x-3\right)}{x\left(x-3\right)-2\left(x-3\right)}$ (using ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)$)
$⇒\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}$
$⇒\frac{\left(x+3\right)}{\left(x-2\right)}$ (cancelled (x−3) from the numerator and denominator)
So,
$\frac{{x}^{2}-9}{{x}^{2}-5x+6}=\frac{\left(x+3\right)}{\left(x-2\right)}$

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