Chapter 7: Q. 134 (page 668)

In the following exercises, perform indicated operations.
$\frac{4}{x^{2} - 6 x + 5} - \frac{3}{x^{2} - 7 x + 10}$

Short Answer

Expert verified

The required expression is $\begin{array}{rcl} \frac{1}{(x - 1) (x - 2)} \end{array}$

Step by step solution

Step 1. Given information

The given expression is $\frac{4}{x^{2} - 6 x + 5} - \frac{3}{x^{2} - 7 x + 10}$

Step 2. Find LCD

Factor the denominators of the given rational expressions.

$\begin{array}{rcl} x^{2} - 6 x + 5 & = & (x - 5) (x - 1) \\ x^{2} - 7 x + 10 & = & (x - 5) (x - 2) \end{array}$

So, the LCD is $(x - 5) (x - 1) (x - 2)$

Step 3. Express with LCD

Rewrite the expression in terms of LCD.

$\frac{4}{x^{2} - 6 x + 5} - \frac{3}{x^{2} - 7 x + 10} = \frac{4 x - 8}{(x - 5) (x - 1) (x - 2)} - \frac{3 x - 3}{(x - 5) (x - 1) (x - 2)}$

Stp 4. Simplify

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

$\begin{array}{rcl} \frac{4 x - 8 - 3 x + 3}{(x - 5) (x - 1) (x - 2)} & = & \frac{x - 5}{(x - 5) (x - 1) (x - 2)} \\ = & \frac{1}{(x - 1) (x - 2)} \end{array}$

So, the required expression is $\begin{array}{rcl} \frac{1}{(x - 1) (x - 2)} \end{array}$ .

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In the following exercises, perform indicated operations.
$\frac{4}{x^{2} - 6 x + 5} - \frac{3}{x^{2} - 7 x + 10}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Express with LCD

Stp 4. Simplify

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In the following exercises, perform indicated operations.4x2-6x+5-3x2-7x+10

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Express with LCD

Stp 4. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Probability and Statistics

Applied Mathematics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{4}{x^{2} - 6 x + 5} - \frac{3}{x^{2} - 7 x + 10}$