Chapter 7: Q. 42 (page 652)

In the following exercises, multiply the rational expressions.
$\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} . \frac{n^{2} - 10 n + 25}{2 n^{2} - 13 n + 21}$

Short Answer

Expert verified

The simplified rational expression is $\frac{- (n + 2) (n - 5)}{(n + 5) (n - 3)}$

Step by step solution

Step 1. Given Information

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

We have to multiply the given rational expression.

Step 2. Factor the numerators and denominators

$= \frac{(2 n - 7) (n + 2)}{(5 + n) (5 - n)} . \frac{(n - 5) (n - 5)}{(2 n - 7) (n - 3)} = \frac{(2 n - 7) (n + 2) (n - 5) (n - 5)}{- (5 + n) (n - 5) (2 n - 7) (n - 3)}$

Step 3. Remove the common factors and simplify

$= \frac{- (n + 2) (n - 5)}{(n + 5) (n - 3)}$

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In the following exercises, multiply the rational expressions.
$\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} . \frac{n^{2} - 10 n + 25}{2 n^{2} - 13 n + 21}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the numerators and denominators

Step 3. Remove the common factors and simplify

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In the following exercises, multiply the rational expressions.2n2-3n-1425-n2.n2-10n+252n2-13n+21

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the numerators and denominators

Step 3. Remove the common factors and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, multiply the rational expressions.
$\frac{2 n^{2} - 3 n - 14}{25 - n^{2}} . \frac{n^{2} - 10 n + 25}{2 n^{2} - 13 n + 21}$