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

How do you solve a rational equation?

Back

To solve a rational equation, find a common denominator, eliminate the fractions by multiplying both sides by that denominator, and then solve the resulting polynomial equation.

Front

What is the first step in solving the equation \( \frac{1}{x-2} = 3 \)?

Back

The first step is to multiply both sides by \( x-2 \) to eliminate the fraction.

Front

What does it mean to check for extraneous solutions?

Back

Checking for extraneous solutions means verifying that the solutions obtained do not make any denominator in the original equation equal to zero.

Front

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

Back

x = 5.

Front

What is the importance of finding a common denominator in rational equations?

Back

Finding a common denominator allows you to combine fractions and simplify the equation, making it easier to solve.

Front

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

Back

x = \frac{1}{5}.

Front

What is an example of a rational expression?

Back

An example of a rational expression is \( \frac{x^2 - 1}{x + 1} \).

Front

What happens if you multiply both sides of a rational equation by zero?

Back

Multiplying by zero is undefined and can lead to incorrect solutions, so it should be avoided.

Front

Solve for x: \( \frac{x-4}{2} = \frac{3}{4} \)

Back

x = 5.