Chapter 7: Q.500. (page 742)

Given $f (x) = \frac{x - 4}{x^{2} - 3 x - 10}$ and $g (x) = \frac{x - 5}{x^{2} - 2 x - 8}$ .
Find $R (x) = f (x) \div g (x)$ .

Short Answer

Expert verified

The solution is $\frac{(x - 4) (x - 4)}{(x - 5) (x - 5)}$ .

Step by step solution

Step 1. Given information.

The given functions are $f (x) = \frac{x - 4}{x^{2} - 3 x - 10}$ and $g (x) = \frac{x - 5}{x^{2} - 2 x - 8}$ .

Step 2. Simplify the expression.

$R (x) = f (x) \div g (x) R (x) = \frac{x - 4}{x^{2} - 3 x - 10} \div \frac{x - 5}{x^{2} - 2 x - 8} R (x) = \frac{(x - 4)}{(x + 2) (x - 5)} \div \frac{(x - 5)}{(x + 2) (x - 4)} R (x) = \frac{(x - 4)}{(x + 2) (x - 5)} \times \frac{(x + 2) (x - 4)}{(x - 5)} (R e m o v e t h e c o m m o n f a c t o r) R (x) = \frac{(x - 4) (x - 4)}{(x - 5) (x - 5)}$

Step 3. Simplified answer.

Hence, the simplified expression is $R (x) = \frac{(x - 4) (x - 4)}{(x - 5) (x - 5)}$ .

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Given $f (x) = \frac{x - 4}{x^{2} - 3 x - 10}$ and $g (x) = \frac{x - 5}{x^{2} - 2 x - 8}$ .
Find $R (x) = f (x) \div g (x)$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Simplified answer.

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Given fx=x-4x2-3x-10and gx=x-5x2-2x-8.FindRx=fx÷gx.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Given $f (x) = \frac{x - 4}{x^{2} - 3 x - 10}$ and $g (x) = \frac{x - 5}{x^{2} - 2 x - 8}$ .
Find $R (x) = f (x) \div g (x)$ .