Question

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

Answer 1

`(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)`