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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

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

01

Step 1. Given information

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

02

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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Most popular questions from this chapter

Accident investigation: The skid marks for a car involved in an accident measured 216 feet. Use the formula $s = \sqrt{24 d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

In the following exercises, simplify by rationalizing the denominator

$\frac{\sqrt{3}}{\sqrt{m} - \sqrt{5}}$

In the following exercises, simplify by rationalizing the denominator

(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$

In the following exercises, solve.

$\sqrt{6 v - 2} - 10 = 0$ .

Try It.

Solve: $\sqrt{x} + 3 = \sqrt{x + 5}$

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