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mikey3 · Mar 19, 2014, 06:48 PM

Find the following product. Be sure your answer is in simplest form.

(5b+10)/a * a/5b-15

I am completely lost. I tried to cancel out both of the 5b, and reduce the 10 and -15 by 5 and got 10/-15 then 2/-3 What am I doing wrong?

ebaines · Mar 20, 2014, 05:41 AM

First thing you're doing wrong is not using parentheses correctly. What you wrote is this:

$\frac {(5b+10)}a \times \frac a {5b} -15$

but I suspect what you meant is this:

$\frac {(5b+10)}{a} \times \frac {a} {(5b-15)}$

Please confirm that I have that right.

You can't cance the b's, because of the +10 term in the first numerator as well as the -15 term in the second denominator. But you can the a's, then divide through by 5:

$\frac {5b+10}{\cancel a} \cdot \frac {\cancel a} {5b-15} = \frac {5b+10}{5b-15} = \frac {\cancel 5 (b+2)}{\cancel 5 (b-3)} = \frac {b+2}{b-3}$