Question 1

$\frac{5-\mathrm{x}}{\mathrm{x}}-\frac{7}{\mathrm{x}}=-\frac{3}{4}$

Accepted Answer

A)  $\{8\}$ 
B)  $\{-4\}$ 
C)  $\{-8\}$. 
D)  $\varnothing$ 
A)  $\{8\}$ 
B)  $\{-4\}$ 
C)  $\{-8\}$. 
D)  $\varnothing$

Question 2

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function.
-$f(x)=\frac{2}{x+3}$

Accepted Answer

A)  vertical asymptote: $\mathrm{x}=2$; holes: none 
B)  vertical asymptote: $\mathrm{x}=3$; holes: none 
C)  vertical asymptote: $\mathrm{x}=-2$; holes: none 
D)  vertical asymptote: $\mathrm{x}=-3$; holes: none 
A)  vertical asymptote: $\mathrm{x}=2$; holes: none 
B)  vertical asymptote: $\mathrm{x}=3$; holes: none 
C)  vertical asymptote: $\mathrm{x}=-2$; holes: none 
D)  vertical asymptote: $\mathrm{x}=-3$; holes: none

Question 3

Find all values $x$ such that $r(x)=0$.

Accepted Answer

A)  0 
B)  -3 
C)  $-3,3$ 
D)  3
Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function. 
A)  0 
B)  -3 
C)  $-3,3$ 
D)  3
Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function.

Question 4

Simplify the complex fraction.
-$\frac{\frac{1}{5}-\frac{1}{x}}{\frac{5-x}{5}}$

Accepted Answer

A)  $\frac{1}{x}$ 
B)  $-\frac{1}{x}$ 
C)  $-x$ 
D)  $-\frac{5}{x}$ 
A)  $\frac{1}{x}$ 
B)  $-\frac{1}{x}$ 
C)  $-x$ 
D)  $-\frac{5}{x}$

Question 5

$\frac{x+3}{x-4} \div \frac{x+7}{x-7}$

Accepted Answer

A)  $\frac{(x+3)(x-7)}{(x-4)(x+7)}$ 
B)  $\frac{(\mathrm{x}-4)(\mathrm{x}+7)}{(\mathrm{x}+3)(\mathrm{x}-7)}$ 
C)  $\frac{(x+3)(x+7)}{(x-4)(x-7)}$ 
D)  $\frac{(\mathrm{x}-4)(\mathrm{x}-7)}{(\mathrm{x}+3)(\mathrm{x}+7)}$ 
A)  $\frac{(x+3)(x-7)}{(x-4)(x+7)}$ 
B)  $\frac{(\mathrm{x}-4)(\mathrm{x}+7)}{(\mathrm{x}+3)(\mathrm{x}-7)}$ 
C)  $\frac{(x+3)(x+7)}{(x-4)(x-7)}$ 
D)  $\frac{(\mathrm{x}-4)(\mathrm{x}-7)}{(\mathrm{x}+3)(\mathrm{x}+7)}$

Question 6

A water tank can be filled in 8 minutes and emptied in 9 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Accepted Answer

A)  $\frac{1}{72}$ minutes 
B)  72 minutes 
C)  $4 \frac{4}{17}$ minutes 
D)  $\frac{1}{17}$ minutes 
A)  $\frac{1}{72}$ minutes 
B)  72 minutes 
C)  $4 \frac{4}{17}$ minutes 
D)  $\frac{1}{17}$ minutes

Question 7

Simplify the rational expression. (Assume the denominator is nonzero.)
-$\frac{x^{2}-2 x}{(x+3)(x-2)}$

Accepted Answer

A)  $\frac{x-2}{x+3}$ 
B)  $\frac{x^{2}}{x+3}$ 
C)  $\frac{1}{x+3}$ 
D)  $\frac{x}{x+3}$ 
A)  $\frac{x-2}{x+3}$ 
B)  $\frac{x^{2}}{x+3}$ 
C)  $\frac{1}{x+3}$ 
D)  $\frac{x}{x+3}$

Question 8

Solve for the specified variable
-$F=\frac{G m_{1} m_{2}}{d^{2}}$ for $G$

Accepted Answer

A)  $G=\frac{F}{m_{1} m_{2}}$ 
B)  $G=\frac{F^{2}}{m_{1} m_{2}}$ 
C)  $G=\frac{F m_{1} m_{2}}{d^{2}}$ 
D)  $\mathrm{G}=\mathrm{Fd} 2$ 
A)  $G=\frac{F}{m_{1} m_{2}}$ 
B)  $G=\frac{F^{2}}{m_{1} m_{2}}$ 
C)  $G=\frac{F m_{1} m_{2}}{d^{2}}$ 
D)  $\mathrm{G}=\mathrm{Fd} 2$

Question 9

Simplify the rational expression. (Assume the denominator is nonzero.)
-$\frac{x^{2}+6 x-27}{x^{2}+18 x+81}$

Accepted Answer

A)  $\frac{6 x+27}{18 x-18}$ 
B)  $\frac{x-3}{x+9}$ 
C)  $-\frac{x^{2}+6 x-27}{x^{2}+18 x+81}$ 
D)  $\frac{6 x-27}{18 x+81}$ 
A)  $\frac{6 x+27}{18 x-18}$ 
B)  $\frac{x-3}{x+9}$ 
C)  $-\frac{x^{2}+6 x-27}{x^{2}+18 x+81}$ 
D)  $\frac{6 x-27}{18 x+81}$

$\frac{5-\mathrm{x}}{\mathrm{x}}-\frac{7}{\mathrm{x}}=-\frac{3}{4}$

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function. - $f(x)=\frac{2}{x+3}$

Find all values $x$ such that $r(x)=0$ .

Simplify the complex fraction. - $\frac{\frac{1}{5}-\frac{1}{x}}{\frac{5-x}{5}}$

$\frac{x+3}{x-4} \div \frac{x+7}{x-7}$

A water tank can be filled in 8 minutes and emptied in 9 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac{x^{2}-2 x}{(x+3)(x-2)}$

Solve for the specified variable - $F=\frac{G m_{1} m_{2}}{d^{2}}$ for $G$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac{x^{2}+6 x-27}{x^{2}+18 x+81}$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Rational Expressions and Equations

5−xx−7x=−34\frac{5-\mathrm{x}}{\mathrm{x}}-\frac{7}{\mathrm{x}}=-\frac{3}{4}x5−x​−x7​=−43​

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function. - f(x)=2x+3f(x)=\frac{2}{x+3}f(x)=x+32​

Find all values xxx such that r(x)=0r(x)=0r(x)=0 .

Simplify the complex fraction. - 15−1x5−x5\frac{\frac{1}{5}-\frac{1}{x}}{\frac{5-x}{5}}55−x​51​−x1​​

x+3x−4÷x+7x−7\frac{x+3}{x-4} \div \frac{x+7}{x-7}x−4x+3​÷x−7x+7​

A water tank can be filled in 8 minutes and emptied in 9 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Simplify the rational expression. (Assume the denominator is nonzero.) - x2−2x(x+3)(x−2)\frac{x^{2}-2 x}{(x+3)(x-2)}(x+3)(x−2)x2−2x​

Solve for the specified variable - F=Gm1m2d2F=\frac{G m_{1} m_{2}}{d^{2}}F=d2Gm1​m2​​ for GGG

Simplify the rational expression. (Assume the denominator is nonzero.) - x2+6x−27x2+18x+81\frac{x^{2}+6 x-27}{x^{2}+18 x+81}x2+18x+81x2+6x−27​

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

$\frac{5-\mathrm{x}}{\mathrm{x}}-\frac{7}{\mathrm{x}}=-\frac{3}{4}$

Find any vertical asymptotes as well as the location of any holes in the graph of the given rational function. - $f(x)=\frac{2}{x+3}$

Find all values $x$ such that $r(x)=0$ .

Simplify the complex fraction. - $\frac{\frac{1}{5}-\frac{1}{x}}{\frac{5-x}{5}}$

$\frac{x+3}{x-4} \div \frac{x+7}{x-7}$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac{x^{2}-2 x}{(x+3)(x-2)}$

Solve for the specified variable - $F=\frac{G m_{1} m_{2}}{d^{2}}$ for $G$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac{x^{2}+6 x-27}{x^{2}+18 x+81}$