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.

**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 3.15**

**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.

**Example 3.18 **

Simplify

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