Q15. Find the product.a2+2a+1a+1.a鈭�... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q15. (page 699)

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

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 $q 鈮� 0$ .

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

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

$\frac{a}{b} . \frac{c}{d} = \frac{a c}{b d} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� ........... (1)$

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

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

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

Therefore, the final answer is 1.

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91影视

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

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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91影视

Find the product.a2+2a+1a+1.a鈭�1a2鈭�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

Statistics

Calculus

Geometry

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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