Can you do Test 5 number 19 from the no calculator section?

Sure. This is one of those questions that looks worse than it is. All you really need to do is get a common denominator and simplify the given expression. Here’s what you’re starting with:

    \begin{align*}\dfrac{2x+6}{(x+2)^2}-\dfrac{2}{x+2}\end{align*}

All you need to do to have a common denominator is multiply the fraction on the right by \dfrac{x+2}{x+2}!

    \begin{align*}&\dfrac{2x+6}{(x+2)^2}-\dfrac{2(x+2)}{(x+2)^2}\\=&\dfrac{2x+6}{(x+2)^2}-\dfrac{2x+4}{(x+2)^2}\\=&\dfrac{2x+6-(2x+4)}{(x+2)^2}\\=&\dfrac{2}{(x+2)^2}\end{align*}

So there you have it, the a in \dfrac{a}{(x+2)^2} is 2.

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