Solving 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 does it mean for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero, as division by zero is not possible.

Front

Solve for x: \frac{x}{2} = 5

Back

x = 10

Front

Solve for x: \frac{3}{x-1} = 1

Back

x = 4

Front

What is the first step in solving \frac{1}{x} + \frac{1}{x+2} = \frac{3}{2}?

Back

The first step is to find a common denominator, which is 2x(x+2).

Front

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

Back

x = 7

Front

What is the importance of checking your solution in rational equations?

Back

Checking your solution is important to ensure that it does not make any denominator zero, which would invalidate the solution.

Front

Solve for x: \frac{2x}{x+1} = 4

Back

x = 6/2 = 3

Front

What is a common mistake when solving rational equations?

Back

A common mistake is forgetting to check for extraneous solutions that may arise from multiplying both sides by a variable expression.