Chapter 7: Q135E. (page 668)

In the following exercise, perform the indicated operation:
$\frac{5}{x^{2} + 8 x - 9} - \frac{4}{x^{2} + 10 x + 9}$

Short Answer

Expert verified

$\frac{1}{(x - 1) (x + 1)}$

Step by step solution

Step 1. Given information.

The following expression is given:

$\frac{5}{x^{2} + 8 x - 9} - \frac{4}{x^{2} + 10 x + 9}$

Step 2. Simplification of the given expression.

Factor the denominators:

$\frac{5}{(x + 9) (x - 1)} - \frac{4}{(x + 9) (x + 1)}$

Find the LCD of the denominators:

$(x + 9) (x - 1) (x + 1)$

Rewrite the expressions with the LCD at the denominator:

$\frac{5 (x + 1)}{(x + 9) (x - 1) (x + 1)} - \frac{4 (x - 1)}{(x + 9) (x + 1) (x - 1)}$

Simplify:

$\frac{5 (x + 1) - 4 (x - 1)}{(x + 9) (x - 1) (x + 1)} \frac{5 x + 5 - 4 x + 4}{(x + 9) (x - 1) (x + 1)}$

Simplify and cancel the common factors from the numerator and the denominator:

$\frac{(x + 9)}{(x + 9) (x - 1) (x + 1)} \frac{1}{(x - 1) (x + 1)}$

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In the following exercise, perform the indicated operation:
$\frac{5}{x^{2} + 8 x - 9} - \frac{4}{x^{2} + 10 x + 9}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the given expression.

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In the following exercise, perform the indicated operation:5x2+8x-9-4x2+10x+9

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplification of the given expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Calculus

Pure Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercise, perform the indicated operation:
$\frac{5}{x^{2} + 8 x - 9} - \frac{4}{x^{2} + 10 x + 9}$