Question

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

Answer 1

`=>(t-5)/(t-4)`

Explanation:

`(t^2-25) / (t^2+t-20)`

`={(t+5)(t-5)}/{(t+5)(t-4)}`

We can cancel the `t+5` terms

`={cancel{(t+5)}(t-5)}/{cancel{(t+5)}(t-4)}`

`=(t-5)/(t-4)`

Answer 2

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

Explanation:

Simplify:

`(t^2-25)/(t^2+t-20)`

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

`(a^2+b^2)=(a+b)(a-b)`,

where:

`a=t^2` and `b=5^2`.

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

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

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

Cancel `t+5`.

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

`(t-5)/(t-4)`