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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 .