Chapter 7: Q.489. (page 742)

Perform the indicated operation and simplify.
$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$

Short Answer

Expert verified

The solution 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. Simplify the expression.

$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} + \frac{n^{2} - 7 n - 1}{n^{2} - 1} \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{2 n^{2} + 8 n - 1 + n^{2} - 7 n - 1}{n^{2} - 1} \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{2 n^{2} + n^{2} + 8 n - 7 n - 1 - 1}{n^{2} - 1} \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{3 n^{2} + n - 2}{(n^{2} - 1)} \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{3 n^{2} + 3 n - 2 n - 2}{n^{2} - 1} \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{3 n (n + 1) - 2 (n + 1)}{(n - 1) (n + 1)} \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{(n + 1) (3 n - 2)}{(n - 1) (n + 1)} (R e m o v e t h e c o m m o n f a c t o r) \frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} = \frac{3 n - 2}{n - 1}$

Step 3. Simplified answer.

Hence, the simplified expression is $\frac{3 n - 2}{n - 1}$ .

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Perform the indicated operation and simplify.
$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Simplified answer.

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Perform the indicated operation and simplify.2n2+8n-1n2-1-n2-7n-11-n2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

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Perform the indicated operation and simplify.
$\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}}$