# How do you simplify (t^2-25)/(t^2+t-20)?

May 18, 2018

$\implies \frac{t - 5}{t - 4}$

#### Explanation:

$\frac{{t}^{2} - 25}{{t}^{2} + t - 20}$

$= \frac{\left(t + 5\right) \left(t - 5\right)}{\left(t + 5\right) \left(t - 4\right)}$

We can cancel the $t + 5$ terms

$= \frac{\cancel{\left(t + 5\right)} \left(t - 5\right)}{\cancel{\left(t + 5\right)} \left(t - 4\right)}$

$= \frac{t - 5}{t - 4}$

May 18, 2018

(t^2-25)/(t^2+t-20)=color(blue)((t-5)/(t-4)

#### Explanation:

Simplify:

$\frac{{t}^{2} - 25}{{t}^{2} + t - 20}$

Factor the numerator using the formula for a difference of squares:

$\left({a}^{2} + {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$,

where:

$a = {t}^{2}$ and $b = {5}^{2}$.

(t^2-5^2)=color(red)((t+5)color(green)((t-5))

$\frac{\textcolor{red}{\left(t + 5\right) \textcolor{g r e e n}{\left(t - 5\right)}}}{{t}^{2} + t - 20}$

Factor the denominator.

Find two numbers that when added equal $1$ and when multiplied equal $- 20$. The numbers $- 4$ and $5$ meet the requirements.

${t}^{2} + t - 20 = \textcolor{red}{\left(t + 5\right)} \textcolor{p u r p \le}{\left(t - 4\right)}$

color(red)((t+5)color(green)((t-5)))/color(red)((t+5)color(purple)((t-4))

Cancel $t + 5$.

$\frac{\cancel{t + 5} \left(t - 5\right)}{\cancel{t + 5} \left(t - 4\right)}$

$\frac{t - 5}{t - 4}$