Chapter 8: Q 124. (page 931)

Divide Rational Expressions: $\{\frac{12 p^{2} + 3 p}{p + 3} \div \frac{p^{2} + 2 p - 63}{p^{2} - p - 12}\} \times \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Short Answer

Expert verified

The required answer is $\frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)}$ .

Step by step solution

Step 1. Given information.

The given expression is $\{\frac{12 p^{2} + 3 p}{p + 3} \div \frac{p^{2} + 2 p - 63}{p^{2} - p - 12}\} \times \frac{p - 7}{9 p^{3} - 9 p^{2}}$ .

Step 2. Simplify the expression.

$\{\frac{12 p^{2} + 3 p}{p + 3} \div \frac{p^{2} + 2 p - 63}{p^{2} - p - 12}\} \times \frac{p - 7}{9 p^{3} - 9 p^{2}} = (\frac{\frac{12 p^{2} + 3 p}{p + 3}}{\frac{p^{2} + 2 p - 63}{p^{2} - p - 12}}) \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Apply the fraction rule.

$= \frac{(12 p^{2} + 3 p) (p^{2} - p - 12)}{(p + 3) (p^{2} + 2 p - 63)} \times \frac{p - 7}{9 p^{3} - 9 p^{2}} = \frac{(12 p^{2} + 3 p) (p - 4) (p + 3)}{(p + 3) (p^{2} + 2 p - 63)} \times \frac{p - 7}{9 p^{3} - 9 p^{2}} = \frac{(12 p^{2} + 3 p) (p - 4) (p - 7)}{(p^{2} + 2 p - 63) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4) (p - 7)}{(p - 7) (p + 9) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4)}{(p + 9) (9 p^{3} - 9 p^{2})}$

Step 3. Factor the numerators and denominators and then multiply.

$\frac{3 p (4 p + 1) (p - 4)}{(p + 9) (9 p^{3} - 9 p^{2})} = \frac{3 p (4 p + 1) (p - 4)}{(p + 9) \times 9 p^{2} (p - 1)} = \frac{3 p (4 p + 1) (p - 4)}{(p + 9) \times 3 \times 3 p^{2} (p - 1)} = \frac{p (4 p + 1) (p - 4)}{(p + 9) \times 3 p^{2} (p - 1)} = \frac{p (4 p + 1) (p - 4)}{(p + 9) \times 3 p p (p - 1)} = \frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)}$

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Divide Rational Expressions: $\{\frac{12 p^{2} + 3 p}{p + 3} \div \frac{p^{2} + 2 p - 63}{p^{2} - p - 12}\} \times \frac{p - 7}{9 p^{3} - 9 p^{2}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Factor the numerators and denominators and then multiply.

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Divide Rational Expressions:12p2 + 3pp + 3÷p2+ 2p − 63p2 − p − 12 ×p − 79p3 − 9p2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Factor the numerators and denominators and then multiply.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\{\frac{12 p^{2} + 3 p}{p + 3} \div \frac{p^{2} + 2 p - 63}{p^{2} - p - 12}\} \times \frac{p - 7}{9 p^{3} - 9 p^{2}}$