Chapter 8: Q 8.88 (page 948)

Add: $\frac{2 n}{n^{2} - 3 n - 10} + \frac{6}{n^{2} + 5 n + 6}$

Short Answer

Expert verified

The addition of the rational expression is $\frac{2 (n^{2} + 6 n - 15)}{(n + 2) (n - 5) (n + 3)}$

Step by step solution

Given information

The given rational expression is $\frac{2 n}{n^{2} - 3 n - 10} + \frac{6}{n^{2} + 5 n + 6}$

The simplification of the rational expression

$\frac{2 n}{n^{2} - 3 n - 10} + \frac{6}{n^{2} + 5 n + 6}$

Factor the denominator

$\frac{2 n}{n^{2} - 5 n + 2 n - 10} + \frac{6}{n^{2} + 3 n + 2 n + 6} \frac{2 n}{n (n - 5) + 2 (n - 5)} + \frac{6}{n (n + 3) + 2 (n + 3)} \frac{2 n}{(n + 2) (n - 5)} + \frac{6}{(n + 2) (n + 3)}$

The LCD of the expression is $(n + 2) (n - 5) (n + 3)$ .

$\frac{2 n (n + 3)}{(n + 2) (n - 5) (n + 3)} + \frac{6 (n - 5)}{(n + 2) (n + 3) (n - 5)} \frac{2 n^{2} + 6 n}{(n + 2) (n - 5) (n + 3)} + \frac{6 n - 30}{(n + 2) (n + 3) (n - 5)} \frac{2 n^{2} + 12 n - 30}{(n + 2) (n - 5) (n + 3)} \frac{2 (n^{2} + 6 n - 15)}{(n + 2) (n - 5) (n + 3)}$

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Add: $\frac{2 n}{n^{2} - 3 n - 10} + \frac{6}{n^{2} + 5 n + 6}$

Short Answer

Step by step solution

Given information

The simplification of the rational expression

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Add:2nn2-3n-10+6n2+5n+6

Short Answer

Step by step solution

Given information

The simplification of the rational expression

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Applied Mathematics

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Logic and Functions

Discrete Mathematics

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Add: $\frac{2 n}{n^{2} - 3 n - 10} + \frac{6}{n^{2} + 5 n + 6}$