Divide. Show all work. Make sure to simplify. Assume no denominator equals zero x^2-144/x^2+7x-60 divided by 3x-36/9x-45

Question

I'm really confused on this and if anyone can help, I'd appreciate it. Thanks!

Answer 1

x^2-144 = (x-12)(x+12)
x^2+7x-60 = (x+12)(x-5)

3x-36 = 3(x-12)
9x-45 = 9(x-5)

So, since dividing by a fraction is the same as multiplying by its reciprocal, we really have

(x-12)(x+12) / (x-5)(x+12) * 9(x-5) / 3(x-12)

Now you can see that almost everything cancels out, leaving you with just a value of

3

There's an (x-12) top and bottom, (x+12) top and bottom, and (x-5) top and bottom.

Answer 2

Thank you! That makes so much more sense now!