Madeline Lott

2022-01-15

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

sukljama2

Beginner2022-01-16Added 32 answers

Step 1

Given,

The expression

$\frac{{x}^{2}-9}{{x}^{2}-5x+6}$

We have to simplify the expression.

Step 2

We have

$\frac{{x}^{2}-9}{{x}^{2}-5x+6}$

$\Rightarrow \frac{{x}^{2}-{3}^{2}}{{x}^{2}-3x-2x+6}$ (done factorization)

$\Rightarrow \frac{(x+3)(x-3)}{x(x-3)-2(x-3)}$ (using ${a}^{2}-{b}^{2}=(a+b)(a-b)$ )

$\Rightarrow \frac{(x+3)(x-3)}{(x-3)(x-2)}$

$\Rightarrow \frac{(x+3)}{(x-2)}$ (cancelled (x−3) from the numerator and denominator)

So,

$\frac{{x}^{2}-9}{{x}^{2}-5x+6}=\frac{(x+3)}{(x-2)}$

Given,

The expression

We have to simplify the expression.

Step 2

We have

So,

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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