Chapter 11: Q20. (page 699)

Find the quotient.
$\frac{x^{2} + 7 x + 12}{x^{2} - 25} \div \frac{x^{2} - 9}{2 x + 10}$

Short Answer

Expert verified

The final answer is $\frac{2 (x + 4)}{(x - 5) (x - 3)}$ .

Step by step solution

Step 1. Define a rational function.

A function of the form $y = \frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q \neq 0$ .

Step 2. Define the quotient of two expressions ab and cd.

The quotient of two expressions $\frac{a}{b}$ and $\frac{c}{d}$ , where $b \neq 0$ and $d \neq 0$ , is given below.

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a c}{b d} ........... (1)$

Step 3. Calculate the quotient x2+7x+12x2−25÷x2−92x+10.

Use $(1)$ to find the quotient $\frac{x^{2} + 7 x + 12}{x^{2} - 25} \div \frac{x^{2} - 9}{2 x + 10}$ .

role="math" localid="1648030191290" $\begin{array}{r} \frac{x^{2} + 7 x + 12}{x^{2} - 25} \div \frac{x^{2} - 9}{2 x + 10} = (\frac{x^{2} + 7 x + 12}{x^{2} - 25}) \times (\frac{2 x + 10}{x^{2} - 9}) \\ = \frac{(x^{2} + 7 x + 12) (2 x + 10)}{(x^{2} - 25) (x^{2} - 9)} \\ = \frac{(x^{2} + 4 x + 3 x + 12) [2 (x + 5)]}{(x^{2} - 5^{2}) (x^{2} - 9)} \\ = \frac{[x (x + 4) + 3 (x + 4)] [2 (x + 5)]}{(x + 5) (x - 5) (x + 3) (x - 3)} \\ = \frac{(x + 4) (x + 3) (2) (x + 5)}{(x + 5) (x - 5) (x + 3) (x - 3)} \\ = \frac{2 (x + 4)}{(x - 5) (x - 3)} \end{array}$

Therefore, the final answer is $\frac{2 (x + 4)}{(x - 5) (x - 3)}$ .

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Find the quotient.
$\frac{x^{2} + 7 x + 12}{x^{2} - 25} \div \frac{x^{2} - 9}{2 x + 10}$

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the quotient of two expressions ab and cd.

Step 3. Calculate the quotient x2+7x+12x2−25÷x2−92x+10.

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Find the quotient.x2+7x+12x2−25÷x2−92x+10

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the quotient of two expressions ab and cd.

Step 3. Calculate the quotient x2+7x+12x2−25÷x2−92x+10.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Probability and Statistics

Mechanics Maths

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Find the quotient.
$\frac{x^{2} + 7 x + 12}{x^{2} - 25} \div \frac{x^{2} - 9}{2 x + 10}$