Chapter 8: Q 8.78 (page 944)

Rewrite as equivalent rational expressions with denominator
$(x + 3) (x + 5) (x + 6)$
$\frac{x}{x^{2} + 8 x + 15}, \frac{5}{x^{2} + 9 x + 18}$ .

Short Answer

Expert verified

The simplification of the expression is $\frac{x^{2} + 6 x}{(x + 3) (x + 5) (x + 6)}, \frac{5 x + 25}{(x + 3) (x + 5) (x + 6)}$

Step by step solution

Given information

The given rational expression is $\frac{x}{x^{2} + 8 x + 15}, \frac{5}{x^{2} + 9 x + 18}$ .

The simplification of the expression

$\frac{x}{x^{2} + 5 x + 3 x + 15}, \frac{5}{x^{2} + 9 x + 18}$

Factorize the denominator

role="math" localid="1648482456775" $\frac{x}{x^{2} + 5 x + 3 x + 15}, \frac{5}{x^{2} + 6 x + 3 x + 18} \frac{x}{x (x + 5) + 3 (x + 5)}, \frac{5}{x (x + 6) + 3 (x + 6)} \frac{x}{(x + 3) (x + 5)}, \frac{5}{(x + 3) (x + 6)}$

The LCD of the denominator $(x + 3) (x + 5) (x + 6)$ .

$\frac{x (x + 6)}{(x + 3) (x + 5) (x + 6)}, \frac{5 (x + 5)}{(x + 3) (x + 5) (x + 6)} S i m p l i f y t h e n u m e r a t o r \frac{x^{2} + 6 x}{(x + 3) (x + 5) (x + 6)}, \frac{5 x + 25}{(x + 3) (x + 5) (x + 6)}$

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Rewrite as equivalent rational expressions with denominator
$(x + 3) (x + 5) (x + 6)$
$\frac{x}{x^{2} + 8 x + 15}, \frac{5}{x^{2} + 9 x + 18}$ .

Short Answer

Step by step solution

Given information

The simplification of the expression

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Rewrite as equivalent rational expressions with denominatorx+3x+5x+6xx2+8x+15,5x2+9x+18.

Short Answer

Step by step solution

Given information

The simplification of the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Calculus

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Rewrite as equivalent rational expressions with denominator
$(x + 3) (x + 5) (x + 6)$
$\frac{x}{x^{2} + 8 x + 15}, \frac{5}{x^{2} + 9 x + 18}$ .