How do you simplify #(t^2-25)/(t^2+t-20)#?
1 Answer
Oct 8, 2015
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)/(t-4)#