Chapter 8: Q 8.55. (page 928)

Divide: $\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}}$ .

Short Answer

Expert verified

The required answer is $\frac{x + 2}{4}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}}$

Step 2. Simplify the expression.

$\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}}$

Rewrite with division sign,

$\frac{3 x^{2} + 7 x + 2}{4 x + 24} \div \frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}$

Rewrite the division as the product of the first rational expression and the reciprocal of the second.

$\frac{3 x^{2} + 7 x + 2}{4 x + 24} \cdot \frac{x^{2} + x - 30}{3 x^{2} - 14 x - 5}$

Factor the numerators and denominators and then multiply.

$\frac{(3 x + 1) (x + 2)}{4 (x + 6)} \cdot \frac{(x - 5) (x + 6)}{(3 x + 1) (x - 5)} \frac{(3 x + 1) (x + 2) (x - 5) (x + 6)}{4 (x + 6) (3 x + 1) (x - 5)}$

Simplify by dividing out common factors.

$\frac{x + 2}{4}$

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Divide: $\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

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Divide:3x2+7x+24x+243x2-14x-5x2+x-30.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Divide: $\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}}$ .