Answered: Fill in the blank/s: The restrictions…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Fill in the blank/s:

The restrictions on the variable in the rationalequation 1/(x - 2) -2/(x + 4) =(2x - 1)/(x² + 2x - 8) are_________and ___________?

Expert Solution

Step 1

Consider the given rational equation,

$\frac{1}{(x - 2)} - \frac{2}{(x + 4)} = \frac{(2 x - 1)}{(x^{2} + 2 x - 8)}$

here the objective is to find the restrictions on the variable.

The value of the variables is not acceptable at which the denominator of the rational equation is zero,.

simplify the given rational equation as follows,

$\begin{array}{rcl} \frac{1}{(x - 2)} - \frac{2}{(x + 4)} & = & \frac{(2 x - 1)}{(x - 2) (x + 4)} \\ \frac{x + 4 - 2 x + 4}{(x - 2) (x + 4)} & = & \frac{(2 x - 1)}{(x - 2) (x + 4)} \\ \frac{- x}{(x - 2) (x + 4)} - \frac{(2 x - 1)}{(x - 2) (x + 4)} & = & 0 \\ \frac{- 3 x + 1}{(x - 2) (x + 4)} & = & 0 \end{array}$

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