91Ó°ÊÓ

In the following exercises, evaluate the rational expression for the given values. \(\frac{y^{2}+5 y+6}{y^{2}-1}\) (a) \(y=0\) (b) \(y=2\) (c) \(y=-2\)

In the following exercises, multiply. $$ \frac{3 q^{2}}{q^{2}+q-6} \cdot \frac{q^{2}-9}{9 q} $$

In the following exercises, add. $$ \frac{2}{15}+\frac{7}{15} $$

In the following exercises, subtract. $$ \frac{z^{2}+6 z}{z^{2}-25}-\frac{3 z+20}{25-z^{2}} $$

In the following exercises, find the LCD. $$ \frac{4}{b^{2}+6 b+9}, \frac{2 b}{b^{2}-2 b-15} $$

Kayaking When Trina kayaks upriver, it takes her \(\frac{5}{3-c}\) hours to go 5 miles, where \(c\) is the speed of the river current. It takes her \(\frac{5}{3+c}\) hours to kayak 5 miles down the river. (a) Find an expression for the number of hours it would take Trina to kayak 5 miles up the river and then return by adding \(\frac{5}{3-c}+\frac{5}{3+c}\). (b) Evaluate your answer to part (a) when \(c=1\) to find the number of hours it would take Trina if the speed of the river current is 1 mile per hour.

Efraim wants to start simplifying the complex fraction \(\frac{\frac{1}{a}+\frac{1}{b}}{\frac{1}{a}-\frac{1}{b}}\) by cancelling the variables from the numerator and denominator. Explain what is wrong with Efraim's plan.

In the following exercises, solve. $$ \frac{56}{72}=\frac{y}{9} $$

One 12 ounce can of soda has 150 calories. If Josiah drinks the big 32 ounce size from the local mini-mart, how many calories does he get?

Steve changed \(\$ 600\) into 480 Euros. How many Euros did he receive for each US dollar?