Solving Fractional Equations

Solving Fractional Equations

Solve each fractional equation. Remember to check for extraneous solutions.

1. Solve for x: \(\frac{3}{x} + \frac{2}{5} = \frac{1}{x}\)

2. Find the value of y: \(\frac{y}{y+2} - \frac{1}{y} = \frac{2}{y(y+2)}\)

3. Which of the following is an extraneous solution for the equation \(\frac{x}{x-3} = \frac{3}{x-3} + 2\)?

4. When solving fractional equations, the first step is often to find the   of all denominators.

5. A solution that arises from the process of solving an equation but is not a valid solution to the original equation is called an   solution.

6. The equation \(\frac{1}{x-1} = \frac{1}{x+1}\) has no real solutions.