Operations of Rational Expressions
We have studied the concepts of addition, subtraction, multiplication and division of rational numbers in previous classes. Now let us generalize the above for rational expressions.
If are two rational expressions where q (x) ≠ 0, s (x) ≠ 0 ,
their product is
In other words, the product of two rational expression is the product of their numerators divided by the product of their denominators and the resulting expression is then reduced to its lowest form.
If are two rational expressions, where q (x), s (x) ≠ 0 then,
Thus division of one rational expression by other is equivalent to the product of first and reciprocal of the second expression. If the resulting expression is not in its lowest form then reduce to its lowest form.
Example 3.16 Find
(i) Add or Subtract the numerators
(ii) Write the sum or difference of the numerators found in step (i) over the common denominator.
(iii) Reduce the resulting rational expression into its lowest form.
Example 3.17 Find
(i) Determine the Least Common Multiple of the denominator.
(ii) Rewrite each fraction as an equivalent fraction with the LCM obtained in step (i). This is done by multiplying both the numerators and denominator of each expression by any factors needed to obtain the LCM.
(iii) Follow the same steps given for doing addition or subtraction of the rational expression with like denominators.