Question

8.5 divide radical expressions (homework)
score: 12/14 answered: 13/14
question 14
rationalize the denominator. simplify your answer as much as possible.
\\(\frac{9}{\sqrt{a + h}-\sqrt{a}}=\\)
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Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $\sqrt{a + h}+\sqrt{a}$.
\[
\frac{9}{\sqrt{a + h}-\sqrt{a}}\times\frac{\sqrt{a + h}+\sqrt{a}}{\sqrt{a + h}+\sqrt{a}}
\]

Step2: Expand denominator

Use the difference - of - squares formula $(x - y)(x + y)=x^{2}-y^{2}$. Here $x=\sqrt{a + h}$ and $y = \sqrt{a}$, so the denominator is $(\sqrt{a + h})^{2}-(\sqrt{a})^{2}=a + h-a=h$.
The expression becomes $\frac{9(\sqrt{a + h}+\sqrt{a})}{h}$.

Answer:

$\frac{9(\sqrt{a + h}+\sqrt{a})}{h}$