Reduce $\displaystyle\frac{x^2-9}{x-3}$

Reduce $\displaystyle\frac{y^2-5y-6}{y^2-1}$

Reduce $\displaystyle\frac{2a^3-16}{4a^2-12a+8}$

Reduce $\displaystyle\frac{x^2-3x+ax-3a}{x^2-ax-3x+3a}$

Reduce $\displaystyle\frac{a-b}{b-a}$

Reduce $\displaystyle\frac{x^2-25}{5-x}$

$f(x)=\displaystyle\frac{x-4}{x-2}$, find $f(0)$, $f(-4)$, $f(4)$, $f(-2)$, and $f(2)$.

Find the domain of the following:

1. $f(x)=\displaystyle\frac{x-4}{x-2}$

2. $g(x)=\displaystyle\frac{x^2+5}{x+1}$

3. $h(x)=\displaystyle\frac{x}{x^2-9}$

If $f(x)=3x-5$, find $\displaystyle\frac{f(x)-f(a)}{x-a}$.

If $f(x)=x^2-4$, find $\displaystyle\frac{f(x)-f(a)}{x-a}$.

If $f(x)=3x-5$, find $\displaystyle\frac{f(x+h)-f(x)}{h}$.

If $f(x)=x^2-4$, find $\displaystyle\frac{f(x+h)-f(x)}{h}$

Multiply $\displaystyle\frac{6}{7}\cdot \displaystyle\frac{14}{18}$

Multiply $\displaystyle\frac{8x^3}{27y^8}\cdot \displaystyle\frac{9y^3}{12x^2}$

Multiply $\displaystyle\frac{x-3}{x^2-4}\cdot \displaystyle\frac{x+2}{x^2-6x+9}$

Multiply $\displaystyle\frac{2y^2-4y}{2y^2-2}\cdot \displaystyle\frac{y^2-2y-3}{y^2-5y+6}$

Divide $\displaystyle\frac{6}{8} \div \displaystyle\frac{3}{5}$

Divide $\displaystyle\frac{8x^3}{5y^2}\div \displaystyle\frac{4x^2}{10y^6}$

Divide $\displaystyle\frac{x^2-y^2}{x^2-2xy+y^2}\div \displaystyle\frac{x^3+y^3}{x^3-x^2y}$

Perform the indicated operation.
$\displaystyle\frac{a^2-8a+15}{a+4}\cdot \displaystyle\frac{a+2}{a^2-5a+6}\div \displaystyle\frac{a^2-3a-10}{a^2+2a-8}$

Multiply $\displaystyle\frac{xa+xb+ya+yb}{xa-xb-ya+yb}\cdot \displaystyle\frac{xa+xb-ya-yb}{xa-xb+ya-yb}$

Multiply $\left(4x^2-36\right)\cdot \displaystyle\frac{12}{4x+12}$

Multiply $3(x-2)(x-1)\cdot \displaystyle\frac{5}{x^2 -3x+2}$

Add $\displaystyle\frac{4}{9}+\displaystyle\frac{2}{9}$

Add $\displaystyle\frac{x}{x^2-1}+\displaystyle\frac{1}{x^2-1}$

Subtract $\displaystyle\frac{2x-5}{x-2}-\displaystyle\frac{x-3}{x-2}$

Add $\displaystyle\frac{3}{14}+\displaystyle\frac{7}{30}$

Add $\displaystyle\frac{-2}{x^2-2x-3}+\displaystyle\frac{3}{x^2-9}$

Subtract $\displaystyle\frac{x+4}{2x+10}-\displaystyle\frac{5}{x^2-25}$

Subtract $\displaystyle\frac{2x-2}{x^2+4x+3}-\displaystyle\frac{x-1}{x^2+5x+6}$

Add $\displaystyle\frac{x^2}{x-7}+\displaystyle\frac{6x+7}{7-x}$

Subtract $2-\displaystyle\frac{9}{3x+1}$

Write an expression for the sum of a number and twice its reciprocal. Then simplify the expression.

Simplify: $\displaystyle\frac{\displaystyle\frac{3}{4}}{\displaystyle\frac{5}{8}}$

Simplify: $\displaystyle\frac{\displaystyle\frac{1}{x}+\displaystyle\frac{1}{y}}{\displaystyle\frac{1}{x}-\displaystyle\frac{1}{y}}$

Simplify: $\displaystyle\frac{\displaystyle\frac{x-2}{x^2-9}}{\displaystyle\frac{x^2-4}{x+3}}$

Simplify $\displaystyle\frac{1-\displaystyle\frac{4}{x^2}}{1-\displaystyle\frac{1}{x}-\displaystyle\frac{6}{x^2}}$

Simplify: $2-\displaystyle\frac{3}{x+\displaystyle\frac{1}{3}}$

Solve $\displaystyle\frac{x}{2}-3=\displaystyle\frac{2}{3}$

Solve $\displaystyle\frac{6}{a-4}=\displaystyle\frac{3}{8}$

Solve $\displaystyle\frac{x}{x-2}+\displaystyle\frac{2}{3}=\displaystyle\frac{2}{x-2}$

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

Solve $3+\displaystyle\frac{1}{x}=\displaystyle\frac{10}{x^2}$

Solve $\displaystyle\frac{y-4}{y^2-5y}=\displaystyle\frac{2}{y^2-25}$

Solve for $y$: $x=\displaystyle\frac{y-4}{y-2}$

Solve for $x$: $\displaystyle\frac{1}{x}=\displaystyle\frac{1}{b}+\displaystyle\frac{1}{a}$

Graph $f(x)=\displaystyle\frac{6}{x-2}$

Graph $g(x)=\displaystyle\frac{6}{x+2}$

One number is twice another. The sum of their reciprocal is 2. Find the numbers.

Two families go on a ski trip. The first family makes the $455$-mile trip $5$ miles per hour faster than the second family. The second family takes a half-hour longer. What were the speeds of the two families?

The current of a river is $3$ miles per hour. It takes a boat $3$ hours to travel $12$ miles upstream and return. What is the speed of the boat in still water?

An inlet pipe can fill a pool in $10$ hours and the drain can empty it in $12$ hours. If the pool is empty and both the inlet pipe and drain are open, how long will it take to fill the pool?

Graph $y=\displaystyle\frac{x-4}{x-2}$

Divide $\displaystyle\frac{10x^5-15x^4+20x^3}{5x^2}$

Divide $\dfrac{8x^3y^5-16x^2y^2+4x^4y^3}{-2x^2y}$

Divide $\displaystyle\frac{10a^4b^2+8ab^3-12a^3b+6ab}{4a^2b^2}$

Divide $\displaystyle\frac{x^2-6xy-7y^2}{x+y}$

Divide $\displaystyle\frac{2x^2-7x+9}{x-2}$

$2x-4\overline{\smash{)}4x^3-6x-11}$

Divide $\displaystyle\frac{x^2-6xy-7y^2}{x+y}$

Factor $x^3+9x^2+26x+24$ if $x+2$ is a factor.

Suppose $y$ varies directly as $x$. If $y$ is $15$ and $x$ is $3$, find $y$ when $x$ is $4$.

The distance a skydiver falls is directly proportional to the square of the time he has been falling. If the skydiver falls $64$ feet in the first $2$ seconds.

1. How far will he have fallen after $3.5$ seconds?

2. Graph the relationship between distance and time.

3. How long will it take him to fall $256$ feet?

The volume of a gas is inversely proportional to the pressure of the gas on its container. If the pressure of $48$ psi corresponds to a volume of $50\text{ ft}^3$, what pressure is needed to produce a volume of $100\text{ ft}^3$?

$y$ varies jointly with $x$ and the square of $z$. When $x$ is $5$ and $z$ is $180$. Find $y$ when $x$ is $2$ and $z$ is $4$.

In electricity, the resistance of a cable is directly proportional to its length and inversely proportional to the square of the diameter. If a $100$ foot cable $0.5$ inch in diameter has a resistance of $0.2$ ohm, what will the resistance of a cable made from the same material if it is $200$ feet long with a diameter of $0.25$ inch?