Q. 7.74 Solve:聽yy+8=128y2-64+9.... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.74 (page 688)

Solve: $\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 .$

Short Answer

Expert verified

The solution is $y = 7$

Step by step solution

Step 1. Given.

The given equation is: $\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 .$

Step 2. To find

We have to solve the given equation.

Step 3. Calculation

LCD of the denominators is $(y + 8) (y - 8)$ . Multiply both sides by the LCD and then solve the linear equation. After that check if the solution works.

$\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 \frac{y}{y + 8} (y + 8) (y - 8) = \frac{128}{y^{2} - 64} (y + 8) (y - 8) + 9 (y + 8) (y - 8) y (y - 8) = 128 + 9 (y^{2} - 64) y^{2} - 8 y = 128 + 9 y^{2} - 576 y^{2} - 8 y = 9 y^{2} - 448 9 y^{2} - y^{2} + 8 y - 448 = 0 8 y^{2} + 8 y - 448 = 0 8 (y^{2} + y - 56) = 0 y^{2} + y - 56 = 0 (y + 8) (y - 7) = 0 y = - 8, 7$

For $y = - 8$ ,

$\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 \frac{- 8}{- 8 + 8} = \frac{128}{{(- 8)}^{2} - 64} + 9 \frac{- 8}{0} = \frac{128}{0} + 9$

For $y = - 8$ , denominators are 0. So it is not a solution.

For $y = 7$ ,

$\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 \frac{7}{7 + 8} = \frac{128}{7^{2} - 64} + 9 \frac{7}{15} = \frac{128}{49 - 64} + 9 \frac{7}{15} = \frac{128}{- 15} + 9 \frac{7}{15} = \frac{- 128}{15} + \frac{135}{15} \frac{7}{15} = \frac{- 128 + 135}{15} \frac{7}{15} = \frac{7}{15}$

So, $y = 7$ is a solution.

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91影视

Solve: $\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 .$

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

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91影视

Solve:yy+8=128y2-64+9.

Short Answer

Step by step solution

Step 1. Given.

Step 2. To find

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

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Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve: $\frac{y}{y + 8} = \frac{128}{y^{2} - 64} + 9 .$