How do you combine #\frac { 5} { x + 2} - \frac { 2x } { x ^ { 2} - 4}#?

1 Answer
Farnsworthit
Sep 30, 2017

#(3x-10)/(x^2-4)#

Explanation:

As you probably already know, in order to combine fractions (in this case through subtraction) the denominators have to be the same. Now, if you'll look at #x^2-4# you might notice that it is factorable. In fact, its factors are #(x+2)(x-2)#. Using this information, you can multiply #5/(x+2)# by #(x-2)# which will give you the format #((x-2)(5))/((x-2)(x+2))# which yields #(5x-10)/(x^2-4)-(2x)/(x^2-4)#. As you can see, the denominators match up so we can now subtract. The result is #(3x-10)/(x^2-4)# Hope this helps.

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