Question

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

Answer 1

`(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.