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

Question 86530: divide
2x-6
over
21
divided by
5x-15
over
12
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
Divide it by:
.

.
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
and multiply it by the inversion of to get the answer
to this problem. After the inversion, the original division problem is converted to the
following multiplication problem:
.

.
Before it gets too complicated, let's do some factoring. Note that:
.
factors to and
factors to and
factors to and
factors to
.
Substitute all these factored forms into the appropriate places in the multiplication
problem and it becomes:
.

.
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:
.
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
.
Hope this helps you to understand the division process in this problem.
.

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