Review Exercises

$\frac{b-7}{b^2-25}$

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

$\frac{9m^4}{18m{n}^3}$

$\frac{7v-35}{25-v^2}$

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

$\frac{2y^2+y-3}{4-y^2}·\frac{y^2-4y+4}{2y^2+11y+12}$

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

$\frac{3y^2-12y-63}{4y+3}÷(6y^2-42y)$

$\frac{8a^2+16a}{a-4}·\frac{a^2+2a-24}{a^2+7a+10}÷\frac{2a^2-6a}{a+5}$

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

$\frac{7x^2}{x^2-9}+\frac{21x}{x^2-9}$

$\frac{y^2}{y+11}-\frac{121}{y+11}$

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

$\frac{a^2+3a}{a^2-4}-\frac{3a+8}{4-a^2}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

Curtis 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?

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

Marta and Deb work together writing a book that takes them 90 days. If Marta 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 $x=4.$

If the cost of a pizza varies directly with its diameter, and if an 8” diameter pizza costs $12, how much would a 6” diameter pizza cost?

If $m$ varies inversely with the square of $n,$ when $m=4$ and $n=6$ find $m$ when $n=2.$

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?

$\frac{5x}{x-2}>1$

$\frac{1}{x^2-4x-12}<0$

$\frac{4}{x-2}<\frac{3}{x+1}$

Given the function, $R\left(x\right)=\frac{x+1}{x+3},$ find the values of $x$ that make the function less than or equal to 0.

Tillman is starting his own business by selling tacos at the beach. Accounting for the cost of his food truck and ingredients for the tacos, the function $C(x)=2x+\mathrm{6,000}$ represents the cost for Tillman to produce $x,$ tacos. Find ⓐ the average cost function, $c(x)$ for Tillman’s Tacos ⓑ how many tacos should Tillman produce so that the average cost is less than $4.