Chapter 8: Q 238 (page 954)

Add $\frac{3 p}{p^{2} + 4 p - 12} + \frac{1}{p^{2} + p - 30}$ .

Short Answer

Expert verified

The sum is $\frac{3 p^{2} - 14 p - 2}{(p + 6) (p - 5) (p - 2)}$ .

Step by step solution

Given Information

The Given expression is $\frac{3 p}{p^{2} + 4 p - 12} + \frac{1}{p^{2} + p - 30}$ .

Find the LCD of denominators.

Factor the denominators.

$p^{2} + 4 p - 12 = (p + 6) (p - 2)$

$p^{2} + p - 30 = (p + 6) (p - 5)$

LCD $= (p + 6) (p - 5) (p - 2)$

Rewrite the expression in factored form.

$= \frac{3 p}{(p + 6) (p - 2)} + \frac{1}{(p + 6) (p - 5)}$

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{3 p (p - 5)}{(p + 6) (p - 5) (p - 2)} + \frac{1 (p - 2)}{(p + 6) (p - 5) (p - 2)}$

$= \frac{3 p^{2} - 15 p}{(p + 6) (p - 5) (p - 2)} + \frac{p - 2}{(p + 6) (p - 5) (p - 2)}$

Add

Take common denominator.

$= \frac{3 p^{2} - 15 p + p - 2}{(p + 6) (p - 5) (p - 2)}$

Simplify numerator.

$\frac{3 p^{2} - 14 p - 2}{(p + 6) (p - 5) (p - 2)}$

= \frac{3 p^{2} - 14 p - 2}{(p + 6) (p - 5) (p - 2)}

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Add $\frac{3 p}{p^{2} + 4 p - 12} + \frac{1}{p^{2} + p - 30}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Add

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Add3pp2+4p-12+1p2+p-30.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Add

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Applied Mathematics

Statistics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Add $\frac{3 p}{p^{2} + 4 p - 12} + \frac{1}{p^{2} + p - 30}$ .