Chapter 11: Q15. (page 699)

Find the product.
$\frac{a^{2} + 2 a + 1}{a + 1} . \frac{a - 1}{a^{2} - 1}$

Short Answer

Expert verified

The final answer is 1.

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 product of two expressions ab and cd.

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

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

Step 3. Calculate the product a2+2a+1a+1.a−1a2−1.

Use $(1)$ to find the product $\frac{a^{2} + 2 a + 1}{a + 1} . \frac{a - 1}{a^{2} - 1}$ .

$\begin{array}{l} \frac{a^{2} + 2 a + 1}{a + 1} . \frac{a - 1}{a^{2} - 1} = \frac{(a^{2} + 2 a + 1) (a - 1)}{(a + 1) (a^{2} - 1)} \\ = \frac{(a^{2} + 2 (a) (1) + 1^{2}) (a - 1)}{(a + 1) (a^{2} - 1^{2})} \\ = \frac{{(a + 1)}^{2} (a - 1)}{(a + 1) (a + 1) (a - 1)} \\ = \frac{{(a + 1)}^{2} (a - 1)}{{(a + 1)}^{2} (a - 1)} \\ = 1 \end{array}$

Therefore, the final answer is 1.

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Find the product.
$\frac{a^{2} + 2 a + 1}{a + 1} . \frac{a - 1}{a^{2} - 1}$

Short Answer

Step by step solution

Step 1. Define a rational function.

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

Step 3. Calculate the product a2+2a+1a+1.a−1a2−1.

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$x$	$y$
2	8
4	4
8	2
16	1

Find the product.a2+2a+1a+1.a−1a2−1

Short Answer

Step by step solution

Step 1. Define a rational function.

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

Step 3. Calculate the product a2+2a+1a+1.a−1a2−1.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the product.
$\frac{a^{2} + 2 a + 1}{a + 1} . \frac{a - 1}{a^{2} - 1}$