Math CentralQuandaries & Queries


Question from Fatima, a parent:

Hi ,teacher gave two question to my daughter as follows
Solve 2/x+3=(1/xx-9)-(1/x-3)and
Solve (4/x-2)-(x/x+2)=16/xx-4
What should I do ?I should find the value of x by simplifying them or I should use partial fractions or any other method .
In the question she didn't mention any method Only solve the following is given.
Please help me
Thanks & regards fatima

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.


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