Mathematics » Rational Expressions and Equations » Simplify Rational Expressions

# Evaluating Rational Expressions

## Evaluating Rational Expressions

To evaluate a rational expression, we substitute values of the variables into the expression and simplify, just as we have for many other expressions in this book.

## Example

Evaluate $$\frac{2x+3}{3x-5}$$ for each value:

(a) $$x=0$$
(b) $$x=2$$
(c) $$x=-3$$

### Solution

(a)
 Simplify.
(b)
 Simplify.
(c)
 Simplify.

## Example

Evaluate $$\frac{{x}^{2}+8x+7}{{x}^{2}-4}$$ for each value:

(a) $$x=0$$
(b) $$x=2$$
(c) $$x=-1$$

### Solution

(a)
 Simplify.
(b)
 Simplify. This rational expression is undefined for x = 2.
(c)
 Simplify.

Remember that a fraction is simplified when it has no common factors, other than 1, in its numerator and denominator. When we evaluate a rational expression, we make sure to simplify the resulting fraction.

## Example

Evaluate $$\frac{{a}^{2}+2ab+{b}^{2}}{3a{b}^{3}}$$ for each value:

(a) $$a=1,b=2$$
(b) $$a=-2,b=-1$$
(c) $$a=\frac{1}{3},b=0$$

### Solution

(a)
 $$\frac{{a}^{2}+2ab+{b}^{2}}{3a{b}^{2}}$$ when $$a=1,b=2$$. Simplify.
(b)
 $$\frac{{a}^{2}+2ab+{b}^{2}}{3a{b}^{2}}$$ when $$a=-2,b=-1$$. Simplify.
(c)
 $$\frac{{a}^{2}+2ab+{b}^{2}}{3a{b}^{2}}$$ when $$a=\frac{1}{3},b=0$$. Simplify. The expression is undefined.