Chapter 8: Q. 338 (page 982)

In the following exercises, solve
$\frac{p}{p + 7} = \frac{98}{p^{2} - 49} + 8$

Short Answer

Expert verified

The solution is $p = 6, - 7 .$

Step by step solution

Step 1. Given Information

The given rational expression is $\frac{p}{p + 7} = \frac{98}{p^{2} - 49} + 8$

Step 2. Least Common Denominator

The LCD of the equation is $(p + 7) (p - 7)$

Multiply the equation by the LCD,

$(p + 7) (p - 7) \frac{p}{p + 7} = [\frac{98}{p^{2} - 49} + 8] (p + 7) (p - 7) p (p - 7) = 98 + 8 (p + 7) (p - 7) p^{2} - 7 p = 98 + 8 (p^{2} - 49) p^{2} - 7 p = 98 + 8 p^{2} - 392 7 p^{2} + 7 p - 294 = 0 7 (p^{2} + p - 42) = 0$

Step 3. Solution of the equation

On simplifying,

$7 (p^{2} + p - 42) = 0 7 (p^{2} + 7 p - 6 p - 42) = 0 7 (p + 7) (p - 6) = 0 T h e r e f o r e, p + 7 = 0; p - 6 = 0 p = - 7, p = 6$

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In the following exercises, solve
$\frac{p}{p + 7} = \frac{98}{p^{2} - 49} + 8$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Least Common Denominator

Step 3. Solution of the equation

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In the following exercises, solvepp+7=98p2-49+8

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Least Common Denominator

Step 3. Solution of the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Calculus

Geometry

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve
$\frac{p}{p + 7} = \frac{98}{p^{2} - 49} + 8$