Chapter 11: Q21. (page 731)

Find each sum or difference.
$\frac{1}{x - 6} + \frac{3}{x - 2}$

Short Answer

Expert verified

$\frac{4 x - 20}{(x - 6) (x - 2)}$

Step by step solution

Step 1. Multiply.

Multiply numerator and denominator of $\frac{1}{x - 6}$ by $(x - 2)$ .

$\frac{1}{x - 6} \cdot \frac{(x - 2)}{(x - 2)} = \frac{x - 2}{(x - 6) (x - 2)}$

Step 2. Multiply.

Multiply numerator and denominator of $\frac{1}{x - 2}$ by $(x - 6)$ .

$\frac{3}{x - 2} \cdot \frac{(x - 6)}{(x - 6)} = \frac{3 (x - 6)}{(x - 2) (x - 6)}$

Step 3. Add.

Add two expressions obtained above.

$\frac{x - 2}{(x - 6) (x - 2)} + \frac{3 (x - 6)}{(x - 6) (x - 2)} = \frac{x - 2 + 3 (x - 6)}{(x - 6) (x - 2)}$

role="math" localid="1648021441019" $= \frac{x - 2 + 3 x - 18}{(x - 6) (x - 2)} = \frac{4 x - 20}{(x - 6) (x - 2)}$

Therefore, the sum of given expression is $\frac{4 x - 20}{(x - 6) (x - 2)}$ .

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Find each sum or difference.
$\frac{1}{x - 6} + \frac{3}{x - 2}$

Short Answer

Step by step solution

Step 1. Multiply.

Step 2. Multiply.

Step 3. Add.

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Find each sum or difference.1x−6+3x−2

Short Answer

Step by step solution

Step 1. Multiply.

Step 2. Multiply.

Step 3. Add.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

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Study anywhere. Anytime. Across all devices.

Find each sum or difference.
$\frac{1}{x - 6} + \frac{3}{x - 2}$