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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 396 (page 735)

Find $R (x) = \frac{f (x)}{g (x)}$ , where
$f (x) = \frac{27 x^{2}}{3 x - 21} g (x) = \frac{9 x^{2} + 54 x}{x^{2} - x - 42}$

Short Answer

Expert verified

The value of $R (x) = x$

Step by step solution

01

Step. 1 Given Information

Expressions: $f (x) = \frac{27 x^{2}}{3 x - 21} g (x) = \frac{9 x^{2} + 54 x}{x^{2} - x - 42}$

we have find $R (x) = \frac{f (x)}{g (x)}$

02

Step 2. To find R(x),divide f(x) by g(x)

$\frac{f (x)}{g (x)} = \frac{\frac{27 x^{2}}{3 x - 21}}{\frac{9 x^{2} + 54 x}{x^{2} - x - 42}}$

03

Step 3. Rewrite the complex fraction as division

$\frac{27 x^{2}}{3 x - 21} 梅 \frac{9 x^{2} + 54 x}{x^{2} - x - 42}$

04

Step 4. Rewrite as the product of first times the reciprocal of the second.

$\frac{27 x^{2}}{3 x - 21} . \frac{x^{2} - x - 42}{9 x^{2} + 54 x}$

05

Step 5. Factorize the denominator and numerator

$\frac{27 x^{2}}{3 (x - 7)} . \frac{x^{2} - 7 x + 6 x - 42}{9 x (x + 6)} = \frac{27 x^{2}}{3 (x - 7)} . \frac{x (x - 7) + 6 (x - 7)}{9 x (x + 6)} = \frac{27 x^{2}}{3 (x - 7)} . \frac{(x + 6) (x - 7)}{9 x (x + 6)}$

06

Step 6. Multiply and remove common factors

$\frac{27 x^{2} (x + 6) (x - 7)}{27 x (x + 6) (x - 7)} = x$

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