Solve rational equations

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and denominator are polynomials.

Front

What does it mean to solve a rational equation by cross-multiplying?

Back

Cross-multiplying involves multiplying the numerator of one side of the equation by the denominator of the other side to eliminate the fractions.

Front

What is an extraneous solution?

Back

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

Front

How do you check for extraneous solutions in rational equations?

Back

To check for extraneous solutions, substitute the solution back into the original equation to see if it holds true.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify any restrictions on the variable that would make the denominator zero.

Front

What is the solution to the equation 1/(x+4) = 1/5?

Back

x = -4.

Front

How do you solve the equation 2/(x-3) = 1/4?

Back

Cross-multiply to get 2*4 = 1*(x-3), which simplifies to x = 11.

Front

What is the solution to the equation 3/(x+1) = 2/(x-2)?

Back

Cross-multiply to find x = -4.

Front

What does it mean if a rational equation has no solution?

Back

It means that there are no values for the variable that satisfy the equation, often due to contradictions.

Front

What is the solution to the equation (x-1)/(x+2) = 3/4?

Back

x = 5/3.