Chapter 1

Perform the indicated operations and simplify. \(\frac{1+\frac{x}{y}}{1-\frac{x^{2}}{y^{2}}}\)

Suppose \(\boldsymbol{a}\) and \(\boldsymbol{b}\) are real numbers other than 0 and \(a>b\). State whether the inequality is true or false. $$ \frac{1}{a}>\frac{1}{b} $$

Solve the equation by using the quadratic formula. $$ 8(2 m+3)^{2}+14(2 m+3)-15=0 $$

Write the expression in simplest radical form. $$ \sqrt{45} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(3 x^{-1}\right)^{2}\left(4 y^{-1}\right)^{3}(2 z)^{-2} $$

Solve the equation for the indicated variable. $$ w=\frac{k u v}{s^{2}} ; u $$

Indicate whether the statement is true or false. $$ a \div(b \div c)=(a \div b) \div c $$

Perform the indicated operations and simplify. $$ (3 r+4 s)(3 r-4 s) $$

Perform the indicated operations and simplify. \(\frac{\frac{1}{x^{2}}-\frac{1}{y^{2}}}{x+y}\)

Suppose \(\boldsymbol{a}\) and \(\boldsymbol{b}\) are real numbers other than 0 and \(a>b\). State whether the inequality is true or false. $$ a^{3}>b^{3} $$

Solve the equation by using the quadratic formula. $$ 6 w-13 \sqrt{w}+6=0 $$

Write the expression in simplest radical form. $$ \sqrt[3]{-54} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(a^{2} b^{-3}\right)^{2}\left(a^{-2} b^{2}\right)^{-3} $$

Solve the equation for the indicated variable. $$ V=\frac{a x}{x+b} ; x $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 2 x^{3}+6 x+x^{2}+3 $$

Perform the indicated operations and simplify. $$ (2 x-1)^{2}+3 x-2\left(x^{2}+1\right)+3 $$

Perform the indicated operations and simplify. \(\frac{\frac{1}{x^{3}}-\frac{1}{y^{3}}}{\frac{1}{x}-\frac{1}{y}}\)

Suppose \(\boldsymbol{a}\) and \(\boldsymbol{b}\) are real numbers other than 0 and \(a>b\). State whether the inequality is true or false. $$ -a<-b $$

Solve the equation by using the quadratic formula. $$ \left(\frac{t}{t-1}\right)^{2}-\frac{2 t}{t-1}-3=0 $$

Write the expression in simplest radical form. $$ -\sqrt[4]{48} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(5 u^{2} v^{-3}\right)^{-1} \cdot 3\left(2 u^{2} v^{2}\right)^{-2} $$

Solve the equation for the indicated variable. $$ V=C\left(1-\frac{n}{N}\right) ; n $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 2 u^{4}-4 u^{2}+2 u^{2}-4 $$

Perform the indicated operations and simplify. $$ (3 m+2)^{2}-2 m(1-m)-4 $$

Perform the indicated operations and simplify. \(\frac{\frac{1}{2(x+h)}-\frac{1}{2 x}}{h}\)

Write the inequality \(|x-a|

Solve the equation. \begin{equation} \frac{2}{x+3}-\frac{4}{x}=4 \end{equation}

Write the expression in simplest radical form. $$ \sqrt{16 x^{2} y^{3}} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left[\left(\frac{a^{-2} b^{-2}}{3 a^{-1} b^{2}}\right)^{2}\right]^{-1} $$

Solve the equation for the indicated variable. $$ r=\frac{2 m I}{B(n+1)} ; m $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 3 a x+6 a y+b x+2 b y $$

Perform the indicated operations and simplify. $$ (2 x+3 y)^{2}-(2 y+1)(3 x-2)+2(x-y) $$

Perform the indicated operations and simplify. \(\frac{\frac{1}{(x+h)^{2}}-\frac{1}{x^{2}}}{h}\)

Solve the equation. \begin{equation} \frac{3 y-1}{4}+\frac{4}{y+1}=\frac{5}{2} \end{equation}

Write the expression in simplest radical form. $$ \sqrt{40 a^{3} b^{4}} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left[\left(\frac{x^{2} y^{-3} z^{-4}}{x^{-2} y^{-1} z^{2}}\right)^{-2}\right]^{3} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 6 u x-4 u y+3 v x-2 v y $$

Perform the indicated operations and simplify. $$ (x-2 y)(y+3 x)-2 x y+3(x+y-1) $$

Solve the equation. $$ x+2-\frac{3}{2 x-1}=0 $$

Write the expression in simplest radical form. $$ \sqrt[3]{m^{6} n^{3} p^{12}} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(\frac{3^{2} u^{-2} v^{2}}{2^{2} u^{3} v^{-3}}\right)^{-2}\left(\frac{3^{2} v^{5}}{4^{2} u}\right)^{2} $$

The simple interest \(I\) (in dollars) earned when \(P\) dollars is invested for a term of \(t\) yr is given by \(I=\) Prt, where \(r\) is the (simple) interest rate/year. Solve for \(t\) in terms of \(I, P\), and \(r\). If Susan invests $$\$ 1000$$ in a bank paying interest at the rate of \(6 \%\) /year, how long must she leave it in the bank before it earns an interest of $$\$ 90$$ ?

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ u^{4}-v^{4} $$

Perform the indicated operations and simplify. $$ \left(t^{2}-2 t+4\right)\left(2 t^{2}+1\right) $$

Determine whether the statement is true for all real numbers \(a\) and \(b\). $$ \left|b^{2}\right|=b^{2} $$

Solve the equation. $$ \frac{x^{2}}{x-1}=\frac{3-2 x}{x-1} $$

Write the expression in simplest radical form. $$ \sqrt[3]{-27 p^{2} q^{3} r^{4}} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left[\left(-\frac{2^{2} x^{-2} y^{0}}{3^{2} x^{3} y^{-2}}\right)^{-2}\right]^{-2} $$

The relationship between the temperature in degrees Fahrenheit \(\left({ }^{\circ} \mathrm{F}\right)\) and the temperature in degrees Celsius \(\left({ }^{\circ} \mathrm{C}\right)\) is \(F=\frac{9}{5} C+32\). Solve for \(C\) in terms of \(F\). Then use the result to find the temperature in degrees Celsius corresponding to a temperature of \(70^{\circ} \mathrm{F}\).

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ u^{4}-u^{2} v^{2}-6 v^{4} $$