Solve and Simplify Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its simplest form by canceling common factors in the numerator and denominator.

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

How do you find the values that make a rational expression undefined?

Back

Set the denominator equal to zero and solve for the variable.

Front

What is cross-multiplication?

Back

Cross-multiplication is a method used to solve equations of the form a/b = c/d by multiplying the numerator of one fraction by the denominator of the other.

Front

If x/(x-3) = 2, what is x?

Back

x = 6.

Front

What is the solution to the equation 1/(x+4) = 0?

Back

No solution, because a fraction is never equal to zero.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that satisfy the equation.

Front

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

Back

Cross-multiply to get 3 = (x-2), then solve for x to find x = 5.

Front

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

Back

To ensure that the solution does not make any denominator zero, which would make the expression undefined.