SOLUTION: In need of help with this rational exp? (18x+9) over (24x-36) divided by (12x + 6) over (20x-30)

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Question 211864: In need of help with this rational exp?
(18x+9) over (24x-36)
divided by
(12x + 6) over (20x-30)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2818x%2B9%29%2F%2824x-36%29%29%2F%28%2812x+%2B+6%29%2F%2820x-30%29%29
This is an expression and all we can do with an expression is simplify it.

Since fractions represent a division and since divisions can be changed into a multiplication by the reciprocal of the divisor, we can rewrite the above into a multiplication by the reciprocal of the "big" denominator:
%28%2818x%2B9%29%2F%2824x-36%29%29%2A%28%2820x-30%29%2F%2812x+%2B+6%29%29

At some point we will try to reduce the fraction by factoring and canceling common factors. It is easier to do this now than it would be to multiply the numerators and denominators and then factor and cancel. Fortunately each numerator and denominator is fairly simple to factor. They each have a Greatest Common Factor (GCF) we can factor out:

Factoring the GCF's (so you can see clearly the common factors we will cancel):

Now cancel the common factors. (Since this is a multiplication of fractions we can "cross-cancel" factors.):

This leaves:
%281%2F%282%2A2%29%29%2A%285%2F1%29
which simplifies to:
5%2F4