Question 86530
Given:
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{{{(2x - 6)/21}}}
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Divide it by:
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{{{(5x - 15)/12}}}
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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
{{{(2x - 6)/21}}} and multiply it by the inversion of {{{(5x - 15)/12}}} to get the answer
to this problem. After the inversion, the original division problem is converted to the
following multiplication problem:
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{{{((2x - 6)/21)*(12/(5x-15))}}}
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Before it gets too complicated, let's do some factoring. Note that:
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{{{2x - 6}}} factors to {{{2*(x - 3)}}} and
{{{ 21}}} factors to {{{7*3}}} and
{{{12}}} factors to {{{4*3}}} and
{{{5x - 15}}} factors to {{{5*(x-3)}}}
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Substitute all these factored forms into the appropriate places in the multiplication
problem and it becomes:
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{{{((2*(x-3))/(7*3))*((4*3)/(5*(x-3)))}}}
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Cancel all the terms that appear in the numerator with a corresponding appearance in
the denominator as follows:
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{{{2*(cross(x-3))/(7*(cross(3)))*4*(cross(3))/(5*(cross(x-3)))}}}
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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:
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{{{8/35}}} 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 {{{8/35}}}
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Hope this helps you to understand the division process in this problem.
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