Are x=3 and x=-2 solutions to the equation \displaystyle{\frac{2}{x}}=\displaystyle{\frac{x-1}{3}}?

Explain how you know.

Solve each equation algebraically.

\displaystyle{\frac{x+3}{x-1}}=0

Solve each equation algebraically.

\displaystyle{\frac{x+3}{x-1}}=2

Solve each equation algebraically.

\displaystyle{\frac{x+3}{x-1}}=2x+1

Solve each equation algebraically. Then verify your solution using graphing technology.

\displaystyle{\frac{3}{3x+2}}=\displaystyle{\frac{6}{5x}}

For each rational equation, write a function whose zeros are the solutions.

\displaystyle{\frac{x-3}{x+3}}=2

For each rational equation, write a function whose zeros are the solutions.

\displaystyle{\frac{3x-1}{x}}=\displaystyle{\frac{5}{2}}

For each rational equation, write a function whose zeros are the solutions.

\displaystyle{\frac{x-1}{x}}=\displaystyle{\frac{x+1}{x+3}}

For each rational equation, write a function whose zeros are the solutions.

\displaystyle{\frac{x-2}{x+3}}=\displaystyle{\frac{x-4}{x+5}}

Solve algebraically. Verify your solution using a graphing calculator.

\displaystyle{\frac{x-3}{x+3}}=2

Solve algebraically. Verify your solution using a graphing calculator.

\displaystyle{\frac{3x-1}{x}}=\displaystyle{\frac{5}{2}}

Solve algebraically. Verify your solution using a graphing calculator.

\displaystyle{\frac{x-1}{x}}=\displaystyle{\frac{x+1}{x+3}}

Solve algebraically. Verify your solution using a graphing calculator.

\displaystyle{\frac{x-2}{x+3}}=\displaystyle{\frac{x-4}{x+5}}

Solve each equation algebraically.

\displaystyle{\frac{2}{x}}+\displaystyle{\frac{5}{3}}=\displaystyle{\frac{7}{x}}

Solve each equation algebraically.

\displaystyle{\frac{10}{x+3}}+\displaystyle{\frac{10}{3}}=6

Solve each equation algebraically.

\displaystyle{\frac{2x}{x-3}}=1-\displaystyle{\frac{6}{x-3}}

Solve each equation algebraically.

\displaystyle{\frac{2}{x+1}}+\displaystyle{\frac{1}{x+1}}=3

Solve each equation algebraically.

\displaystyle{\frac{2}{2x+1}}=\displaystyle{\frac{5}{4-x}}

Solve each equation algebraically.

\displaystyle{\frac{5}{x-2}}=\displaystyle{\frac{4}{x+3}}

Solve each equation algebraically.

\displaystyle{\frac{2x}{2x+1}}=\displaystyle{\frac{5}{4-x}}

Solve each equation algebraically.

\displaystyle{\frac{3}{x}}+\displaystyle{\frac{4}{x+1}}=2

Solve each equation algebraically.

\displaystyle{\frac{2x}{5}}=\displaystyle{\frac{x^2-5x}{5x}}

Solve each equation algebraically.

x+\displaystyle{\frac{x}{x-2}}=0

Solve each equation algebraically.

\displaystyle{\frac{1}{x+2}}+\displaystyle{\frac{24}{x+3}}=13

Solve each equation algebraically.

\displaystyle{\frac{-2}{x-1}}=\displaystyle{\frac{x-8}{x+1}}

Solve each equation using graphing technology. Round your answers to two decimal places, if necessary.

\displaystyle{\frac{2}{x+2}}=\displaystyle{\frac{3}{x+6}}

Solve each equation using graphing technology. Round your answers to two decimal places, if necessary.

\displaystyle{\frac{2x-5}{x+10}}=\displaystyle{\frac{1}{x-6}}

Solve each equation using graphing technology. Round your answers to two decimal places, if necessary.

\displaystyle{\frac{1}{x-3}}=\displaystyle{\frac{x+2}{7x+14}}

Solve each equation using graphing technology. Round your answers to two decimal places, if necessary.

\displaystyle{\frac{1}{x}}-\displaystyle{\frac{1}{45}}=\displaystyle{\frac{1}{2x-3}}

Solve each equation using graphing technology. Round your answers to two decimal places, if necessary.

\displaystyle{\frac{2x+3}{3x-1}}=\displaystyle{\frac{x+2}{4}}

Solve each equation using graphing technology. Round your answers to two decimal places, if necessary.

\displaystyle{\frac{1}{x}}=\displaystyle{\frac{2}{x}}+1+\displaystyle{\frac{1}{1-x}}

Use algebra to solve \displaystyle{\frac{x+1}{x-2}}=\displaystyle{\frac{x+3}{x-4}}. Explain your steps.

The Greek mathematician Pythagoras is credited with the discovery of the Golden Rectangle. This is considered to be the rectangle with the dimensions that are the most Visually appealing. In a Golden Rectangle, the length and width are related by the proportion \frac{l}{w} = \frac{w}{l - w}. A billboard with a length of 15 m is going to be built. What must its width be to form a Golden Rectangle?

The Turtledove Chocolate factory has two chocolate machines. Machine A takes s minutes to fill a case with chocolates, and machine B takes s + 10 minutes to fill a case. Working together, the two machines take 15 min to fill a case. Approximately how long does each machine take to fill a case?

Tanya purchased a large box of comic books for $300. She gave 15 of the comic books to her brother and then sold the rest on an Internet website for \$330, making a profit of \$1.50 on each one.

• How many comic books were in the box?
• What was the original price of each comic book?

Polluted water flows into a pond. The concentration of pollutant ,c, in the pond at time t minutes is modelled by the equation \displaystyle c(t) = 9 - 90 000(\frac{1}{10 000 + 3t}) where c is measured in kilograms per cubic metre.

a) When will the concentration of pollutant in the pond reach 6 kg/m^3?

b) What will happen to the concentration of pollutant over time?

Three employees work at a shipping warehouse. Tom can fill an order in s minutes. Paco can fill an order in s -2 minutes. Carl can fill an order in s + 1 minutes. When Tom and Paco work together, they take about 1 minute and 20 seconds to fill an order. When Paco and Carl work together, they take about 1 minute and 30 seconds to fill an order.

a) How long does each person take to fill an order?

b) How long would all three of them, working together, take to fill an order?

Solve \displaystyle \frac{x^2-6x + 5}{x^2 -2x -3} = \frac{2 - 3x}{x^2 + 3x + 3} ,

correct to two decimal places.

Objects A and B move along a straight line. Their positions, 5, with respect to an origin, at 1‘ seconds, are modelled by the following functions:

you may use a graphing device for this Q

Object A: s_1(t) = \frac{7t}{t^2 + 1}

Object B: s_2(t) = t +\frac{5}{t + 2}

When are the objects at the same position?

Objects A and B move along a straight line. Their positions, 5, with respect to an origin, at 1‘ seconds, are modelled by the following functions:

Object A: s_1(t) = \frac{7t}{t^2 + 1}

Object B: s_2(t) = t +\frac{5}{t + 2}

When is object A closer to the origin than object B?