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Dividing Rational Expressions

Dividing a - b by b - a

We can either factor b - a as -1(a - b) to get the common factor a - b, or else use the fact that (a-b) ÷ (b-a) -1, as shown in the next example.


Example 1

Dividing a - b by b - a

Find the product:


Instead of factoring out -1 from m - 4, we divide m - 4 by 4 - m to get -1:

Note that (m - 4) ÷ (4 - m) = -1.
  = -2  


Dividing Rational Expressions

We divide rational numbers by multiplying by the reciprocal or multiplicative inverse of the divisor. For example,

When we divide rational numbers, we use the following definition.


Division of Rational Numbers

If and are rational numbers with , then

We use the same method to divide rational expressions: We invert the divisor and multiply.


Example 2

Dividing rational expressions

Find each quotient.


a) The reciprocal of the divisor .

Invert and multiply.

b) The reciprocal of 4ab3c is

Quotient rule


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