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?