Exam 12: Rational Expressions and Equations

Solve the problem. -The volume $V$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $250 \mathrm{~cm}^{3}$ under a pressure of $18 \mathrm{~kg} / \mathrm{cm}^{2}$ . What will be its volume under a pressure of $36 \mathrm{~kg} / \mathrm{cm}^{2}$ ?

Solve the problem. -The Epson Stylus 850 can print Helen's class project in 12 minutes. The Epson Stylus 500 can print the project in 36 minutes. If the two printers work together, how long would they take to print out the project?

Solve the problem. -The number $G$ of gears a machine can make varies directly as the time $T$ it operates. If it can make 2706 gears in 14 hours, how many gears can it make in 3 hours?

Find an equation of variation in which $y$ varies inversely as $x$ and the following is true. - $y=49$ , when $x=32$

Solve the problem. -It takes 8 hours for 6 people to paint a house. How long will it take 2 people to do the job?

Solve the equation. - $\frac{x}{x-2}-5=\frac{2}{x-2}$

Write the word or phrase that best completes each statement or answers the question -If 8 is substituted for $x$ in the rational expression $\frac{x-8}{x^{2}-64}$ , the result is $\frac{0}{0}$ . Mathematicians have been known to say "Any number divided by itself is 1 ." Does this mean that this expression is equal to 1 for $\mathrm{x}=8$ ? Explain why or why not.

Solve the equation. - $\frac{6}{x}=\frac{5}{x}+8$

Solve the problem. -To determine the number of fish in a lake, a park ranger catches 280 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 36 of them are tagged. Estimate the number of fish in the lake.

Solve the problem. -In a cake recipe, the ratio of milk to flour is $\frac{5}{9}$ . If 4 cups of milk are used, how many cups of flour are used?

Simplify. - $\frac{4 x^{2}-20 x}{12 x^{2}-60 x}$

Solve the problem. -Sven can type 58 words per minute. How many words would he type in $\frac{1}{2}$ hour (30 minutes)?

Write the word or phrase that best completes each statement or answers the question -Explain in your own words how to divide rational expressions. (How would you explain this to a student in this class who was absent from class?).

Solve the equation. - $\frac{6}{x}+\frac{5}{6}=1$

Subtract. Simplify, if possible. - $\frac{18}{23 x}-\frac{6}{23 x}$

Divide and simplify. - $\frac{7 p-7}{p} \div \frac{8 p-8}{5 p^{2}}$

Add. Simplify, if possible. - $\frac{3 x+4}{2 x-3}+\frac{3-7 x}{-3+2 x}$

Simplify. - $\frac{5+\frac{1}{3}}{3-\frac{2}{27}}$

Find the LCM. - $42 x, 6 x^{2}, 7 x^{3}$

Multiply and, if possible, simplify. - $\frac{k^{2}+14 k+48}{k^{2}+16 k+64} \cdot \frac{k^{2}+8 k}{k^{2}+3 k-18}$