solving rational equations

Front

What are the domain restrictions for the rational equation \( \frac{1}{x-2} + \frac{1}{x+1} = 0 \)?

Back

x ≠ 2, x ≠ -1

Front

Solve the equation \( \frac{x}{x-2} = 0 \) for x.

Back

x = 0

Front

What is an extraneous solution in the context of rational equations?

Back

An extraneous solution is a solution that emerges from the algebraic process but does not satisfy the original equation.

Front

Solve and check for extraneous solutions: \( \frac{x-5}{x+2} = 0 \)

Back

x = 5

Front

Solve the equation \( \frac{2x}{x-3} = 4 \).

Back

x = 6

Front

What is the first step in solving a rational equation?

Back

Identify and state the domain restrictions.

Front

Solve the equation \( \frac{x+3}{x-1} = 2 \).

Back

x = 5

Front

What does it mean to check for extraneous solutions?

Back

It means to substitute the solution back into the original equation to verify if it holds true.

Front

Solve the equation \( \frac{x-1}{x+2} = \frac{3}{4} \).

Back

x = 1.

Front

What is the importance of finding the domain of a rational function?

Back

It helps to identify values that would make the denominator zero, which are not allowed.