Simplify the expression (x^2-5x+4)/(x^2-2x+-8)

 Exercise

$\frac{x^2-5x+4}{x^2-2x-8}$

 

Factor the trinomial $x^2-2x-8$ finding two numbers that multiply to form $-8$ and added form $-2$

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

 

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

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

 

Factor the trinomial $x^2-5x+4$ finding two numbers that multiply to form $4$ and added form $-5$

$\begin{matrix}\left(-1\right)\left(-4\right)=4\\ \left(-1\right)+\left(-4\right)=-5\end{matrix}$

 

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

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

 

Simplifying

$\frac{x-1}{x+2}$

$\frac{x-1}{x+2}$

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