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Chapter 5: Q 4. (page 267)

Simplify : $\frac{\frac{1}{x} + 1}{\frac{1}{x^{2}} - 1}$

Short Answer

Expert verified

Simplified answer is $\frac{x}{1 - x}$

Step by step solution

01

Step 1. Given information

Given that $\frac{\frac{1}{x} + 1}{\frac{1}{x^{2}} - 1}$

02

Step 2. Simplification

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

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

$\Rightarrow \frac{\frac{1}{x} + 1}{\frac{1}{x^{2}} - 1} = \frac{x}{1 - x}$

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Most popular questions from this chapter

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ shown in the figure.

(a) $(g \circ f) (- 1)$ (b) $(g \circ f) (0)$ (c) $(f \circ g) (- 1)$ (d) $(f \circ g) (4)$ .

If $f (x) = a^{x}$ , show that $f (- x) = \frac{1}{f (x)}$ .

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = e^{x} - 1$

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = - e^{x}$

solve each equation. Verify your results using a graphing utility.

$3^{x^{2} - 7} = 27^{2 x}$

See all solutions

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