Math CentralQuandaries & Queries


Question from Jessica, a student:

I can't figure out this problem. This is a Algebra problem.  first it says to  Perform the indicated operation and simplify. b/ b2-25 + 5/b+5 -6/b  Need to find the LCD b2 is a b to the 2nd power and the answer looks like this -25(b-6)/b(b+5)(b-5)

Hi Jessica. I've re-written the starting point:

Can you see that b2 - 25 is a difference of squares? That means the first term is a perfect square, the second term is a perfect square and there is a minus between them. Whenever you see this, you know it factors into the sum of the roots times the difference of the roots:

Now that all the denominators are broken into their factors, you can readily find a common denominator by multiplying (b-5)(b+5)(b). So the first term needs a b in the denominator, so you multiply it by b/b, the second term needs two factors: b and b-5, so multiply by both, top and bottom, and so on.

Finally, multiply it out and simplify:

I am showing the same answer you were given. Can you find the error you made?

Hope this helps,
Stephen La Rocque.

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