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

Oct 8, 2015

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

#### Explanation:

Let's simplify both the numerator and denominator separately, we will start with the top:

${t}^{2} - 25$

Using the difference of squares, I come up with the factored form

$\left(t - 5\right) \left(t + 5\right)$

${t}^{2} + t - 20$

If I think to myself the factors of -20 that add to 1, I get the numbers 5 and -4. This brings me to the factored form:

$\left(t - 4\right) \left(t + 5\right)$

Now putting the entire thing together, we have:

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

One commonality is formed between the top and the bottom, and that is $\left(t + 5\right)$ which we can then cancel from the top and the bottom. This leaves us with our answer

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