Q. 322 In the following exercises, solv... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 322 (page 982)

In the following exercises, solve.
$\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{a^{2} - 121}$

Short Answer

Expert verified

The solution of the equation $\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{a^{2} - 121}$ is

$a = \frac{8}{3}$

Step by step solution

Step 1. Given information

The given equation is

$\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{a^{2} - 121}$

Step 2, Variable values for which denominators are zero

Factor all the denominators of the equation

$\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{a^{2} - 121} \frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{(a + 11) (a - 11)}$

Terms of the equation are not defined for $x = 11 & x = - 11$

so $\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{(a + 11) (a - 11)}, x 鈮� 11, x 鈮� - 11$

Step 3. Solution of equation

The least common denominator of all denominators in the equation is $(a + 11) (a - 11)$

multiply both sides of the equation by the least common denominator $(a + 11) (a - 11)$

$(a + 11) (a - 11) (\frac{9}{a + 11} + \frac{6}{a - 11}) = (a + 11) (a - 11) (\frac{7}{a^{2} - 121}) (a - 11) (9) + (a + 11) (6) = 7 9 a - 99 + 6 a + 66 = 7 15 a = 40 a = \frac{8}{3}$

so the solution of the equation is $a = \frac{8}{3}$

Step 4. Verification

Substitute $a = \frac{8}{3}$ in the equation

$\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{a^{2} - 121} \frac{9}{\frac{8}{3} + 11} + \frac{6}{\frac{8}{3} - 11} \overset{?}{=} \frac{7}{{(\frac{8}{3})}^{2} - 121} \frac{9 路 3}{8 + 33} + \frac{6 路 3}{8 - 33} \overset{?}{=} \frac{7 路 9}{64 - 363} \frac{27}{41} - \frac{18}{25} \overset{?}{=} - \frac{63}{1089} \frac{- 63}{1025} = - \frac{63}{1089}$

The left-hand side is equal to the right-hand side so the solution is correct.

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91影视

In the following exercises, solve.
$\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{a^{2} - 121}$

Short Answer

Step by step solution

Step 1. Given information

Step 2, Variable values for which denominators are zero

Step 3. Solution of equation

Step 4. Verification

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91影视

In the following exercises, solve.9a+11+6a-11=7a2-121

Short Answer

Step by step solution

Step 1. Given information

Step 2, Variable values for which denominators are zero

Step 3. Solution of equation

Step 4. Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$\frac{9}{a + 11} + \frac{6}{a - 11} = \frac{7}{a^{2} - 121}$