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

1 Answer
Oct 8, 2015

(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

(t-5)(t+5)

Let's save that for later, and jump to the bottom

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:

(t - 4)(t + 5)

Now putting the entire thing together, we have:

((t-5)cancel((t+5)))/((t-4)cancel((t+5)))

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

(t-5)/(t-4)