Chapter 7: Q. 395 (page 735)

Find $R (x) = f (x) . g (x)$ , where
$f (x) = \frac{9 x^{2} + 9 x}{x^{2} - 3 x - 4} g (x) = \frac{x^{2} - 16}{3 x^{2} + 12 x}$

Short Answer

Expert verified

The value of $R (x) = 3$

Step by step solution

Step 1. Given information

Expression

: $f (x) = \frac{9 x^{2} + 9 x}{x^{2} - 3 x - 4} g (x) = \frac{x^{2} - 16}{3 x^{2} + 12 x}$

$R (x) = f (x) . g (x)$

Step 2. Multiply f(x) and g(x)

$\frac{9 x^{2} + 9 x}{x^{2} - 3 x - 4} . \frac{x^{2} - 16}{3 x^{2} + 12 x}$

Step 3. Factorize numerator and denominator

$\frac{9 x (x + 1)}{x^{2} - 4 x + x - 4} . \frac{(x - 4) (x + 4)}{3 x (x + 4)} = \frac{9 x (x + 1)}{x (x - 4) + 1 (x - 4)} . \frac{(x - 4) (x + 4)}{3 x (x + 4)} = \frac{9 x (x + 1)}{(x + 1) (x - 4)} . \frac{(x - 4) (x + 4)}{3 x (x + 4)}$

Step 4.Multiply and remove common factors

$\frac{9 x (x + 1) (x - 4) (x + 4)}{3 x (x + 1) (x - 4) (x + 4)} = 3$

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Find $R (x) = f (x) . g (x)$ , where
$f (x) = \frac{9 x^{2} + 9 x}{x^{2} - 3 x - 4} g (x) = \frac{x^{2} - 16}{3 x^{2} + 12 x}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Multiply f(x) and g(x)

Step 3. Factorize numerator and denominator

Step 4.Multiply and remove common factors

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Find R(x)=f(x).g(x), where f(x)=9x2+9xx2-3x-4g(x)=x2-163x2+12x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Multiply f(x) and g(x)

Step 3. Factorize numerator and denominator

Step 4.Multiply and remove common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find $R (x) = f (x) . g (x)$ , where
$f (x) = \frac{9 x^{2} + 9 x}{x^{2} - 3 x - 4} g (x) = \frac{x^{2} - 16}{3 x^{2} + 12 x}$