Chapter 9: Q 9.146 (page 1088)

Simplify.
$\begin{array}{rcl} \frac{\sqrt{q} - \sqrt{10}}{\sqrt{q} + \sqrt{10}} \end{array}$

Short Answer

Expert verified

Answer is $\begin{array}{rcl} \frac{q + 10 - 2 \sqrt{10 q}}{q - 10} \end{array}$

Step by step solution

Step 1. Given information

Fraction is $\begin{array}{rcl} \frac{\sqrt{q} - \sqrt{10}}{\sqrt{q} + \sqrt{10}} \end{array}$

Step 2. Explanation

$\begin{array}{rcl} \frac{\sqrt{q} - \sqrt{10}}{\sqrt{q} + \sqrt{10}} & = & \frac{(\sqrt{q} - \sqrt{10}) (\sqrt{q} - \sqrt{10})}{(\sqrt{q} + \sqrt{10}) (\sqrt{q} - \sqrt{10})} \\ = & \frac{q + 10 - 2 \sqrt{10 q}}{q - 10} \end{array}$

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Simplify.
$\begin{array}{rcl} \frac{\sqrt{q} - \sqrt{10}}{\sqrt{q} + \sqrt{10}} \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Simplify.q-10q+10

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Simplify.
$\begin{array}{rcl} \frac{\sqrt{q} - \sqrt{10}}{\sqrt{q} + \sqrt{10}} \end{array}$