Chapter 7: Q. 133 (page 668)

In the following exercises, perform indicated operations.
$\frac{3}{x^{2} - 3 x - 4} - \frac{2}{x^{2} - 5 x + 4}$

Short Answer

Expert verified

The required LCD is $\frac{x - 5}{(x - 4) (x + 1) (x - 1)}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{3}{x^{2} - 3 x - 4} - \frac{2}{x^{2} - 5 x + 4}$ .

Step 2. Find LCD

Factor the denominators of the given rational expressions.

$x^{2} - 3 x - 4 = (x - 4) (x + 1) x^{2} - 5 x + 4 = (x - 4) (x - 1)$

So, the LCD is $(x - 4) (x + 1) (x - 1)$

Step 3. Express with LCD

Express the expression with LCD.

$\frac{3}{x^{2} - 3 x - 4} - \frac{2}{x^{2} - 5 x + 4} = \frac{3 x - 3}{(x - 4) (x + 1) (x - 1)} - \frac{2 x + 2}{(x - 4) (x + 1) (x - 1)}$

Step 4. Simplify

As the denominator is the same for both the terms, perform subtraction in the numerator and place it over the common denominator.

$\frac{3 x - 3 - 2 x - 2}{(x - 4) (x + 1) (x - 1)} = \frac{x - 5}{(x - 4) (x + 1) (x - 1)}$

So, the required expression is $\frac{x - 5}{(x - 4) (x + 1) (x - 1)}$ .

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In the following exercises, perform indicated operations.
$\frac{3}{x^{2} - 3 x - 4} - \frac{2}{x^{2} - 5 x + 4}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find LCD

Step 3. Express with LCD

Step 4. Simplify

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In the following exercises, perform indicated operations.3x2-3x-4-2x2-5x+4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find LCD

Step 3. Express with LCD

Step 4. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Logic and Functions

Pure Maths

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{3}{x^{2} - 3 x - 4} - \frac{2}{x^{2} - 5 x + 4}$