Chapter 8: Q 108. (page 931)

Divide Rational Expressions: $\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} \div \frac{2 n^{2} - 13 n + 21}{n^{2} - 10 n + 25}$

Short Answer

Expert verified

The required answer is $- \frac{(n + 2) (n - 5)}{(5 + n) (n - 3)}$ .

Step by step solution

Step 1. Given information.

The given expression is $\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} \div \frac{2 n^{2} - 13 n + 21}{n^{2} - 10 n + 25}$ .

Step 2. Simplify the expression.

$\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} \div \frac{2 n^{2} - 13 n + 21}{n^{2} - 10 n + 25} = \frac{\frac{2 n^{2} - 3 n - 14}{25 - n^{2}}}{\frac{2 n^{2} - 13 n + 21}{n^{2} - 10 n + 25}}$

Apply the fraction rule.

$\frac{(2 n^{2} - 3 n - 14) (n^{2} - 10 n + 25)}{(25 - n^{2}) (2 n^{2} - 13 n + 21)} = \frac{(n + 2) (2 n - 7) (n^{2} - 10 n + 25)}{(25 - n^{2}) (n - 3) (2 n - 7)} = \frac{(n + 2) (n^{2} - 10 n + 25)}{(25 - n^{2}) (n - 3)} = \frac{(n + 2) {(n - 5)}^{2}}{(25 - n^{2}) (n - 3)} = \frac{(n + 2) {(n - 5)}^{2}}{(5 + n) (5 - n) (n - 3)} = \frac{(n + 2) {(n - 5)}^{2}}{- (5 + n) (n - 5) (n - 3)} = \frac{(n + 2) (n - 5) (n - 5)}{- (5 + n) (n - 5) (n - 3)} = \frac{(n + 2) (n - 5)}{- (5 + n) (n - 3)} = - \frac{(n + 2) (n - 5)}{(5 + n) (n - 3)}$

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Divide Rational Expressions: $\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} \div \frac{2 n^{2} - 13 n + 21}{n^{2} - 10 n + 25}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

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Divide Rational Expressions:2n2 − 3n − 1425 − n2÷2n2 − 13n + 21n2 − 10n + 25

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} \div \frac{2 n^{2} - 13 n + 21}{n^{2} - 10 n + 25}$