Rational Expressions

Remember that a rational number is a number that can be represented by a fraction.

The quotient (fraction) of two algebraic expressions is called a rational expression.

Some examples:

Simplifying Rational Expressions:

Remove (cancel) all common factors in the numerator & denominator
Simplify:
Solution :
Simplify:

Solution:

(cancel the (x -2) factors )

Multiplying Rational Expressions:
Multiply and simplify answer :

Solution: First factor and cancel common factors in numerator and denominator :

we could multiply the numerator and denominator out , but it’s not necessary.

Divide and simplify answer:

Solution: Convert to multiplication by inverting the divisor:

Factor and cancel common factors in numerator and denominator:

Adding / Subtracting Rational Expressions:

Subtract and simplify:

Solution: Rewrite each fraction as a new fraction with the common denominator:

Simplifying Complex Fractions :

Simplify:

Solution: a fraction is simply a division problem so,

is the same as

Simplify:

Solution: we’ll eventually turn this into a division problem, but first let’s simplify the numerator

and denominator separately

and

Therefore,

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