Chapter 8

If \(y\) varies inversely as \(x\) and \(y=5\) when \(x=10,\) find \(y\) when \(x=2\)

Simplify each expression. $$ \frac{x}{x+1}+\frac{3}{x^{2}-4 x-5} $$

ELECTRICITY For Exercises \(9-12\) , use the following information. The current \(I\) in amperes in an electrical circuit with three resistors in series is given by the equation \(I=\frac{V}{R_{1}+R_{2}+R_{3}},\) where \(V\) is the voltage in volts in the circuit and \(R_{1}, R_{2},\) and \(R_{3}\) are the resistances in ohms of the three resistors. What domain and range values are meaningful in the context of the problem?

Simplify each expression. \(\frac{12 p^{2}+6 p-6}{4(p+1)^{2}} \div \frac{6 p-3}{2 p+10}\)

Solve each equation or inequality. Check your solutions. $$ a+1=\frac{6}{a} $$

If \(y\) varies inversely as \(x\) and \(y=16\) when \(x=5,\) find \(y\) when \(x=20\)

Determine the equations of any vertical asymptotes and the values of \(x\) for any holes in the graph of each rational function. $$ f(x)=\frac{2}{x^{2}-5 x+6} $$

Simplify each expression. $$ \frac{x+\frac{x}{3}}{x-\frac{x}{6}} $$

Simplify each expression. \(\frac{x^{2}+6 x+9}{x^{2}+7 x+6} \div \frac{4 x+12}{3 x+3}\)

Solve each equation or inequality. Check your solutions. $$ \frac{9}{t-3}=\frac{t-4}{t-3}+\frac{1}{4} $$

How does the circumference of a circle vary with respect to its radius? What is the constant of variation?

Determine the equations of any vertical asymptotes and the values of \(x\) for any holes in the graph of each rational function. $$ f(x)=\frac{4}{x^{2}+2 x-8} $$

Simplify each expression. $$ \frac{1-\frac{1}{x}}{x-\frac{1}{x}} $$

Simplify each expression. \(\frac{\frac{c^{3} d^{3}}{a}}{\frac{x c^{2} d}{a x^{2}}}\)

Solve each equation or inequality. Check your solutions. $$ \frac{5}{x+1}-\frac{1}{3}=\frac{x+2}{x+1} $$

A map of Alaska is scaled so that 3 inches represents 93 miles. How far apart are Anchorage and Fairbanks if they are 11.6 inches apart on the map?

Determine the equations of any vertical asymptotes and the values of \(x\) for any holes in the graph of each rational function. $$ f(x)=\frac{x+3}{x^{2}+7 x+12} $$

Simplify each expression. $$ \frac{2-\frac{4}{x}}{x-\frac{4}{x}} $$

Simplify each expression. \(\frac{\frac{2 y}{y^{2}-4}}{\frac{3}{y^{2}-4 y+4}}\)

Solve each equation or inequality. Check your solutions. $$ \frac{2}{y+2}-\frac{y}{2-y}=\frac{y^{2}+4}{y^{2}-4} $$

Identify the type of function represented by each equation. Then graph the equation. \(y=-1.5\)

State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. \(\frac{n}{m}=1.5\)

Determine the equations of any vertical asymptotes and the values of \(x\) for any holes in the graph of each rational function. $$ f(x)=\frac{x-5}{x^{2}-4 x-5} $$

Simplify each expression. $$ \frac{x-\frac{x}{2}}{x+\frac{x}{8}} $$

Simplify each expression. \(\frac{30 b c}{12 b^{3}}\)

Identify the type of function represented by each equation. Then graph the equation. \(y=2.5 x\)

State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. \(3=\frac{a}{b}\)

Graph each rational function. $$ f(x)=\frac{1}{x} $$

Simplify each expression. \(\frac{-3 m n^{3}}{21 m^{2} n^{2}}\)

Solve each equation or inequality. Check your solutions. $$ \frac{7}{a+1}>7 $$

Identify the type of function represented by each equation. Then graph the equation. \(y=\sqrt{9 x}\)

State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. \(a=5 b c\)

Find the LCM of each set of polynomials. $$ 10 s^{2}, 35 s^{2} t^{2} $$

Graph each rational function. $$ f(x)=\frac{3}{x} $$

Simplify each expression. \(\frac{5 t-5}{t^{2}-1}\)

Solve each equation or inequality. Check your solutions. $$ \frac{10}{m+1}>5 $$

Identify the type of function represented by each equation. Then graph the equation. \(y=\frac{4}{x}\)

Find the LCM of each set of polynomials. $$ 36 x^{2} y, 20 x y z $$

Graph each rational function. $$ f(x)=\frac{1}{x+2} $$

Simplify each expression. \(\frac{c+5}{2 c+10}\)

Solve each equation or inequality. Check your solutions. $$ 5+\frac{1}{t}>\frac{16}{t} $$

Identify the type of function represented by each equation. Then graph the equation. \(y=\frac{x^{2}-1}{x-1}\)

State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. \(p=\frac{12}{q}\)

Find the LCM of each set of polynomials. $$ 4 w-12,2 w-6 $$

Graph each rational function. $$ f(x)=\frac{-5}{x+1} $$

Simplify each expression. \(\frac{3 t-6}{2-t}\)

Solve each equation or inequality. Check your solutions. $$ 7-\frac{2}{b}<\frac{5}{b} $$

Identify the type of function represented by each equation. Then graph the equation. \(y=3[x]\)

State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation. \(\frac{2.5}{t}=s\)

Find the LCM of each set of polynomials. $$ x^{2}-y^{2}, x^{3}+x^{2} y $$