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

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

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

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

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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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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

Probability and Statistics

Statistics

Applied Mathematics

Geometry

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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