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

1 Answer

Answer:

#(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)#