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.
 

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