SOLUTION: divide 2x-6 over 21 divided by 5x-15 over 12

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Question 86530: divide
2x-6
over
21
divided by
5x-15
over
12

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%282x+-+6%29%2F21
.
Divide it by:
.
%285x+-+15%29%2F12
.
Recall the "arithmetic" rule about fractions. If you are dividing by a fraction you can
invert the divisor and multiply it by the dividend. In this case it means you can take
%282x+-+6%29%2F21 and multiply it by the inversion of %285x+-+15%29%2F12 to get the answer
to this problem. After the inversion, the original division problem is converted to the
following multiplication problem:
.
%28%282x+-+6%29%2F21%29%2A%2812%2F%285x-15%29%29
.
Before it gets too complicated, let's do some factoring. Note that:
.
2x+-+6 factors to 2%2A%28x+-+3%29 and
+21 factors to 7%2A3 and
12 factors to 4%2A3 and
5x+-+15 factors to 5%2A%28x-3%29
.
Substitute all these factored forms into the appropriate places in the multiplication
problem and it becomes:
.
%28%282%2A%28x-3%29%29%2F%287%2A3%29%29%2A%28%284%2A3%29%2F%285%2A%28x-3%29%29%29
.
Cancel all the terms that appear in the numerator with a corresponding appearance in
the denominator as follows:
.

.
The remaining factors in the numerator are 4 and 2. They multiply out to 8. And the remaining
factors in the denominator are 7 and 5 and they multiply out to 35. This makes the answer:
.
8%2F35 and there are no more common factors in the numerator and the denominator.
So this cannot be reduced further and the answer to the original problem is 8%2F35
.
Hope this helps you to understand the division process in this problem.
.