   SEARCH HOME Math Central Quandaries & 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.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.