Dividing Rational Expressions

In the next example we factor the polynomials in the rational expressions.

Example 1

Dividing rational expressions

Find the quotient:

Solution

		Invert and multiply.
		(5 - x) ÷ (x - 5) = -1.
		Divide out the common factors.
		Multiply the factors in the numerator.

Caution

When dividing rational expressions, you can factor the polynomials at any time, but do not reduce until after you have inverted the divisor.

In the next example division is indicated by a fraction bar.

Note that Algebra Solver can easily do all kinds of problems with rational expressions that you enter. Click here for a sample screenshot.

Example 2

Dividing rational expressions

Perform the operations indicated.

Solution

		Invert the divisor.
		Multiply.

		Invert and multiply.
		Factor.
		Reduce.

Multiply by , the reciprocal of 3.