Review Exercises

$\frac{b-3}{b^2-16}$

$\frac{u-3}{u^2-u-30}$

$\frac{q^2-5}{q+3}\text{when q}=7$

$\frac{z^2+2}{4z-z^2}\text{when z}=3$

$\frac{8m^4}{16m{n}^3}$

$\frac{b^2+7b+12}{b^2+8b+16}$

$\frac{d-16}{16-d}$

$\frac{w^2-3w-28}{49-w^2}$

$\frac{2x{y}^2}{8y^3}·\frac{16y}{24x}$

$\frac{5z^2}{5z^2+40z+35}·\frac{z^2-1}{3z}$

$\frac{r^2-16}{4}÷\frac{r^3-64}{2r^2+8r+32}$

$\frac{3y^2-12y-63}{4y+3}÷(6y^2-42y)$

$\frac{8m^2-8m}{m-4}·\frac{m^2+2m-24}{m^2+7m+10}÷\frac{2m^2-6m}{m+5}$

$\frac{4a^2}{2a-1}-\frac{1}{2a-1}$

$\frac{3x}{x-1}+\frac{2}{x-1}$

$\frac{z^2}{z+10}-\frac{100}{z+10}$

$\frac{5t+4t+3}{t^2-25}-\frac{4t^2-8t-32}{t^2-25}$

$\frac{a^2+3a}{a^2-16}-\frac{3a+8}{16-a^2}$

$\frac{8y^2-10y+7}{2y-5}+\frac{2y^2+7y+2}{5-2y}$

$\frac{6}{n^2-4},\frac{2n}{n^2-4n+4}$

Rewrite as equivalent rational expressions with denominator $(m+2)(m-5)(m+4)$:

Rewrite as equivalent rational expressions with denominator $(3p+1)(p+6)(p+8)$:

$\frac{7}{5a}+\frac{3}{2b}$

$\frac{3d}{d^2-9}+\frac{5}{d^2+6d+9}$

$\frac{5q}{p^{2}q-p^2}+\frac{4q}{q^2-1}$

$\frac{\mathrm{-3}w-15}{w^2+w-20}-\frac{w+2}{4-w}$

$\frac{n}{n+3}+\frac{2}{n-3}-\frac{n-9}{n^2-9}$

$\frac{5}{12x^{2}y}+\frac{7}{20x{y}^3}$

$\frac{\frac{2}{5}+\frac{5}{6}}{\frac{1}{3}+\frac{1}{4}}$

$\frac{\frac{2}{m}+\frac{m}{n}}{\frac{n}{m}-\frac{1}{n}}$

$\frac{\frac{3}{a^2}-\frac{1}{b}}{\frac{1}{a}+\frac{1}{b^2}}$

$\frac{\frac{3}{y^2-4y-32}}{\frac{2}{y-8}+\frac{1}{y+4}}$

$1-\frac{2}{m}=\frac{8}{m^2}$

$\frac{3}{q+8}-\frac{2}{q-2}=1$

$\frac{z}{12}+\frac{z+3}{3z}=\frac{1}{z}$

$\frac{1}{x}-\frac{2}{y}=5\text{for}y$

$P=\frac{k}{V}\text{for}V$

$\frac{3}{y}=\frac{9}{5}$

$\frac{t-3}{5}=\frac{t+2}{9}$

Leo went to Mexico over Christmas break and changed $525 dollars into Mexican pesos. At that time, the exchange rate had $1 US is equal to 16.25 Mexican pesos. How many Mexican pesos did he get for his trip?

On a map of Europe, Paris, Rome, and Vienna form a triangle whose sides are shown in the figure below. If the actual distance from Rome to Vienna is 700 miles, find the distance from

1. ⓐ Paris to Rome
2. ⓑ Paris to Vienna

The height of a lighthouse in Pensacola, Florida is 150 feet. Standing next to the statue, 5.5 foot tall Natalie cast a 1.1 foot shadow How long would the shadow of the lighthouse be?

Mark is riding on a plane that can fly 490 miles with a tailwind of 20 mph in the same time that it can fly 350 miles against a tailwind of 20 mph. What is the speed of the plane?

Mark was training for a triathlon. He ran 8 kilometers and biked 32 kilometers in a total of 3 hours. His running speed was 8 kilometers per hour less than his biking speed. What was his running speed?

Lisa takes 3 hours to mow the lawn while her cousin, Barb, takes 2 hours. How long will it take them working together?

Sue and Deb work together writing a book that takes them 90 days. If Sue worked alone it would take her 120 days. How long would it take Deb to write the book alone?

If $y$ varies inversely as $x$, when $y=20$ and $x=2$ find $y$ when $x=4.$

Vanessa is traveling to see her fiancé. The distance, d, varies directly with the speed, v, she drives. If she travels 258 miles driving 60 mph, how far would she travel going 70 mph?

The distance to stop a car varies directly with the square of its speed. It takes 200 feet to stop a car going 50 mph. How many feet would it take to stop a car going 60 mph?

On a string instrument, the length of a string varies inversely with the frequency of its vibrations. If an 11-inch string on a violin has a frequency of 360 cycles per second, what frequency does a 12 inch string have?