# Solve ((x^2-16)/(x-1))/((6x+8+x^2)/(2x-3+x^2))

## \frac{\frac{x^2-16}{x-1}}{\frac{x^2+6x+8}{x^2+2x-3}}

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$\frac{\left(3+x\right)\left(x-4\right)}{2+x}$

## Step by step solution

Problem

$\frac{\frac{x^2-16}{x-1}}{\frac{x^2+6x+8}{x^2+2x-3}}$
1

Simplifying the fraction

$\frac{-3+2x+x^2}{8+6x+x^2}\cdot\frac{x^2-16}{x-1}$
2

Multiplying fractions

$\frac{\left(-3+2x+x^2\right)\left(x^2-16\right)}{\left(8+6x+x^2\right)\left(x-1\right)}$
3

Factor the trinomial $\left(8+6x+x^2\right)$ finding two numbers that multiply to form $8$ and added form $6$

$\begin{matrix}\left(2\right)\left(4\right)=8\\ \left(2\right)+\left(4\right)=6\end{matrix}$
4

Thus

$\frac{\left(-3+2x+x^2\right)\left(x^2-16\right)}{\left(4+x\right)\left(2+x\right)\left(x-1\right)}$
5

Factor the trinomial $\left(-3+2x+x^2\right)$ finding two numbers that multiply to form $-3$ and added form $2$

$\begin{matrix}\left(-1\right)\left(3\right)=-3\\ \left(-1\right)+\left(3\right)=2\end{matrix}$
6

Thus

$\frac{\left(3+x\right)\left(x-1\right)\left(x^2-16\right)}{\left(x-1\right)\left(4+x\right)\left(2+x\right)}$
7

Simplifying the fraction by $x-1$

$\frac{\left(x^2-16\right)\left(3+x\right)}{1\left(4+x\right)\left(2+x\right)}$
8

Rewrite the difference of squares $\left(x^2-16\right)$ as the product of two conjugated binomials

$\frac{\left(3+x\right)\left(x-4\right)\left(4+x\right)}{1\left(4+x\right)\left(2+x\right)}$
9

Simplifying the fraction by $4+x$

$\frac{\left(3+x\right)\left(x-4\right)}{2+x}$

$\frac{\left(3+x\right)\left(x-4\right)}{2+x}$

### Main topic:

Exponent properties

0.46 seconds

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