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| Math Central | Quandaries & Queries |
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Question from Fatima, a parent: Hi ,teacher gave two question to my daughter as follows |
Hi Fatima,
This doesn't look like it but these problems are about factoring, in particular about the difference of squares which says
\[x^2 - a^2 = (x + a)(x - a)\]
The first problem your daughter is to solve is
\[\frac{2}{x + 3} = \frac{1}{x^2 - 9} - \frac{1}{x - 3}\]
Since $x^2 - 9 = x^2 - 3^2 = (x + 3)(x - 3),$ if you multiply both sides of the original equation by $x^3 - 9$ you should then be ably to solve the resulting equation for x.
Penny
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