Question

What is the sum of22 - 4... and 2?+7 + 22+1-291

Answer 1

We are asked to find the sum of the following terms

`(7x)/(x^2-4)\; and\; (2)/(x+2)`

Let us find their sum.

First of all, notice that the following denominator can be factored as

`x^2-4=x^2-2^2=(x-2)(x+2)`

So, the expression becomes

`\begin{gathered} (7x)/((x-2)(x+2))+(2)/(x+2) \\ \end{gathered}`

Add them by taking the LCM

`(7x)/((x-2)(x+2))+(2)/(x+2)=(7x+(x-2)\cdot2)/((x-2)(x+2))`

Simplify the expression

`(7x+(x-2)\cdot2)/((x-2)(x+2))=(7x+2x-4)/((x-2)(x+2))=(9x-4)/((x-2)(x+2))`

Finally, re-write the denominator in the expanded form as it was written before.

`(9x-4)/((x-2)(x+2))=(9x-4)/(x^2-4)`

Therefore, the simplified expression is

`(9x-4)/(x^2-4)`