1Cademy - Evaluating $$\frac{2x+3}{3x-5}$$ for $$x = 0$$, $$x = 2$$, and $$x = -3$$

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Rational Expression

Example

Evaluating $\frac{2x+3}{3x-5}$ for $x = 0$ , $x = 2$ , and $x = -3$

Evaluate the rational expression $\frac{2x+3}{3x-5}$ for three different values of $x$ by substituting each value and simplifying the numerator and denominator separately.

ⓐ When $x = 0$ : Replace $x$ with $0$ to get $\frac{2(0)+3}{3(0)-5}$ . Simplify the numerator: $2(0)+3 = 0+3 = 3$ . Simplify the denominator: $3(0)-5 = 0-5 = -5$ . The result is $\frac{3}{-5} = -\frac{3}{5}$ .

ⓑ When $x = 2$ : Replace $x$ with $2$ to get $\frac{2(2)+3}{3(2)-5}$ . Simplify the numerator: $2(2)+3 = 4+3 = 7$ . Simplify the denominator: $3(2)-5 = 6-5 = 1$ . The result is $\frac{7}{1} = 7$ .

ⓒ When $x = -3$ : Replace $x$ with $-3$ to get $\frac{2(-3)+3}{3(-3)-5}$ . Simplify the numerator: $2(-3)+3 = -6+3 = -3$ . Simplify the denominator: $3(-3)-5 = -9-5 = -14$ . The result is $\frac{-3}{-14} = \frac{3}{14}$ .

This example demonstrates that evaluating a rational expression follows the same substitute-and-simplify process used for any algebraic expression. After substitution, the numerator and denominator are each simplified independently before the resulting fraction is reduced. Part (ⓒ) illustrates that when both the numerator and denominator are negative, the negatives cancel, producing a positive result.

Updated 2026-04-21

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OpenStax Elementary Algebra

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