Multiplying Rational Expression

A rational expression is the ratio of two polynomials. The variables in the polynomial expression should not contain square roots or negative exponents. For example . Here is the numerator and x – 1 is denominator which is never equal to 0. That is x – 1 ≠ 0. This gives x ≠ 1.
 

Example 1: Multiply the rational expressions and

The first rational expression is . Here can be written as - = (5 + x) ( 5 – x)

=

The second rational expression is . Here the denominator can be written as x(x-5).

=

X =

= =

Therefore the product of the given expression is
 

Example 2: Find the product of and

Writing in factors =

= x (x – 7) + 2 ( x – 7)

= (x – 7) ( x+ 2)

Writing in factors =

= x (x – 2) – 1( x- 2)

= ( x- 2) ( x- 1)

Writing in factors = (x + 2) ( x- 2)

x = X

=

There fore the product of and is .