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{4}{\sqrt{z + h}-\sqrt{z}}=\\)
question help: video written example

Explanation:

Step1: Multiply by conjugate

Multiply the fraction $\frac{4}{\sqrt{z + h}-\sqrt{z}}$ by $\frac{\sqrt{z + h}+\sqrt{z}}{\sqrt{z + h}+\sqrt{z}}$. We get $\frac{4(\sqrt{z + h}+\sqrt{z})}{(\sqrt{z + h}-\sqrt{z})(\sqrt{z + h}+\sqrt{z})}$.

Step2: Expand denominator

Using the difference - of - squares formula $(a - b)(a + b)=a^{2}-b^{2}$, where $a=\sqrt{z + h}$ and $b = \sqrt{z}$, the denominator $(\sqrt{z + h}-\sqrt{z})(\sqrt{z + h}+\sqrt{z})=(z + h)-z$.

Step3: Simplify denominator

$(z + h)-z=h$. So the fraction becomes $\frac{4(\sqrt{z + h}+\sqrt{z})}{h}$.

Answer:

$\frac{4(\sqrt{z + h}+\sqrt{z})}{h}$