Q. 7.30 Subtract:2n2+8n-1n2-1-n2-7n-11-n... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.30 (page 658)

Subtract:
$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$

Short Answer

Expert verified

The required result is $\frac{3 n - 2}{n - 1}$

Step by step solution

Step 1. Given information

The given expression is $\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$ .

Step 2. Multiply the second term by -1-1

Multiply the numerator and denominator of the second term by $- 1$ .

$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{- n^{2} + 7 n + 1}{n^{2} - 1}$

Step 3. Subtract the Numerators

As the denominator is same for both the terms, add the numerator and place over the common denominator.
Add the like terms of the numerator

$\begin{array}{rcl} \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{- n^{2} + 7 n + 1}{n^{2} - 1} & = & \frac{2 n^{2} + 8 n - 1 - (- n^{2} + 7 n + 1)}{n^{2} - 1} \\ = & \frac{2 n^{2} + 8 n - 1 + n^{2} - 7 n - 1}{n^{2} - 1} \\ = & \frac{3 n^{2} + n - 2}{n^{2} - 1} \end{array}$

Step 4. Factor the Numerator

Factor the expression in the numerator and then cancel out the common terms from numerator and denominator.

$\frac{3 n^{2} + n - 2}{n^{2} - 1} = \frac{(3 n - 2) (n + 1)}{(n - 1) (n + 1)} = \frac{(3 n - 2) (n + 1)}{(n - 1) (n + 1)} = \frac{3 n - 2}{n - 1}$

So, the resultant expression is $\frac{3 n - 2}{n - 1}$ .

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91影视

Subtract:
$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Multiply the second term by -1-1

Step 3. Subtract the Numerators

Step 4. Factor the Numerator

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91影视

Subtract:2n2+8n-1n2-1-n2-7n-11-n2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Multiply the second term by -1-1

Step 3. Subtract the Numerators

Step 4. Factor the Numerator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Decision Maths

Logic and Functions

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Subtract:
$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$