Exam 6: Rational Expressions and Equations

An experienced accountant can prepare a tax return in 8 hours. A novice accountant can do the job in 16 hours. How long will it take them to do the job working together?

$\frac{x+2}{x^{2}-1}+\frac{x-3}{x^{2}+3 x-4}=\frac{2 x-3}{x^{2}+5 x+4}$

Find all values of the variable for which the rational expression is undefined. - $\frac{x^{2}+2 x-35}{x^{2}-64}$

$\frac{x-6}{(x+2)^{2}} \cdot \frac{x^{2}-4 x-12}{(x-6)^{2}}$

The intensity I of light varies inversely as the square of the distance $D$ from the source. If the intensity of illumination on a screen 5 feet from a light is 4 foot candles, find the intensity on a screen 20 feet from the light.

Solve for the specified variable - $S=\frac{H}{m t_{1}-m t_{2}}$ for $m$

Find the missing numerator and denominator. - $\frac{(\mathrm{x}-2)(\mathrm{x}-6)}{(\mathrm{x}-1)(\mathrm{x}-9)} \cdot \frac{?}{?}=\frac{(\mathrm{x}-6)(\mathrm{x}-3)}{(\mathrm{x}-1)(\mathrm{x}-4)}$

For the given rational functions $f(x)$ and $g(x), f(x)$ - $g(x)$ . - $f(x)=\frac{6}{5-x}, g(x)=\frac{4}{x-5}$

Find the LCD of the given rational expressions. - $\frac{4}{x^{2}+5 x}, \frac{3}{x^{2}+2 x-15}$

Identify the given function as a linear function, a - $f(x)=x^{2}+2 x-8$

$\mathrm{y}$ varies jointly as $\mathrm{x}$ and $\mathrm{z}$ . If $\mathrm{y}=882$ when $\mathrm{x}=7$ and $\mathrm{z}=18$ , find $\mathrm{y}$ when $\mathrm{x}=6$ and $\mathrm{z}=3$ .

Find the domain of the rational function - $r(x)=\frac{x^{2}-10 x+24}{x^{2}-6 x}$

$\frac{x^{2}-9}{x^{2}+4 x+4} \div \frac{3 x-9}{x^{2}-3 x-10}$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ , and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$ . - $f(x)=\frac{1}{x^{4}}$

Find all values $x$ such that $r(x)=3$ .

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac{x^{2}-64}{x+8}$

$\frac{(2 \mathrm{x}-5)(\mathrm{x}+2)}{(\mathrm{x}+8)(\mathrm{x}-3)} \div \frac{(\mathrm{x}+2)(3 \mathrm{x}+5)}{(\mathrm{x}+8)(\mathrm{x}-3)}$

$\frac{6}{(x+2)^{2}}+\frac{8}{x+2}$

For the given rational functions $f(x)$ and $g(x), f(x)+g(x)$ . - $f(x)=\frac{x+3}{x^{2}-3 x-4}, g(x)=\frac{3 x+2}{x^{2}-4 x-5}$