91Ó°ÊÓ

Perform the indicated operations. Simplify when possible $$ \frac{3 y}{y^{2}-7 y+10}-\frac{2 y}{y^{2}-8 y+15} $$

Perform the indicated operations. Simplify when possible $$ \frac{n}{3 n^{2}+7 n-6}-\frac{1}{3 n^{2}-5 n+2} $$

Do addition, subtraction, and multiplication of polynomials always result in a polynomial? Does division? Why or why not?

Solve. If no solution exists, state this. $$ \frac{1-2 x}{x+2}+\frac{20}{x^{2}-4}=\frac{2 x+1}{2-x} $$

Simplify. If possible, use a second method or evaluation as a check. $$ \frac{\frac{y}{y^{2}-1}-\frac{3 y}{y^{2}+5 y+4}}{\frac{3 y}{y^{2}-1}-\frac{y}{y^{2}-4 y+3}} $$

Divide and, if possible, simplify. $$ \frac{3 a+15}{a^{9}} \div \frac{a+5}{a^{8}} $$

The number of calories burned while dancing is directly proportional to the time spent. It takes 25 min to burn 110 calories. How long would it take to burn 176 calories when dancing?

A Coast Guard plane has enough fuel to fly for \(6 \mathrm{hr},\) and its speed in still air is \(240 \mathrm{mph}\). The plane departs with a 40 -mph tailwind and returns to the same airport flying into the same wind. How far can the plane travel under these conditions?

Divide and, if possible, simplify. $$ \frac{25 x^{2}-4}{x^{2}-9} \div \frac{2-5 x}{x+3} $$

The amount of salt needed per season to control ice on roadways varies directly as the number of storms. During a winter with 8 storms, Green County used 1200 tons of salt on roadways. How many tons would they need during a winter with 4 storms?