Simplifying Rational Expressions Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Simplify 2x2+5xโˆ’3x2+4x+3\frac{2x^2 + 5x - 3}{x^2 + 4x + 3}.

Solution

  1. 1
    Numerator: 2x2+5xโˆ’3=(2xโˆ’1)(x+3)2x^2 + 5x - 3 = (2x - 1)(x + 3). Denominator: x2+4x+3=(x+1)(x+3)x^2 + 4x + 3 = (x + 1)(x + 3).
  2. 2
    Cancel (x+3)(x+3): 2xโˆ’1x+1\frac{2x - 1}{x + 1}, xโ‰ โˆ’3x \neq -3.

Answer

2xโˆ’1x+1\frac{2x - 1}{x + 1}, xโ‰ โˆ’3x \neq -3
Both the numerator and denominator need factoring (the numerator uses the AC method). After finding the common factor (x+3)(x+3), cancel it and note the restriction.

About Simplifying Rational Expressions

Simplifying a rational expression p(x)q(x)\frac{p(x)}{q(x)} by factoring both the numerator and denominator, then canceling common factors. The domain must exclude values that make any original denominator zero.

Learn more about Simplifying Rational Expressions โ†’

More Simplifying Rational Expressions Examples

Example 1 medium

Simplify [formula].

Example 2 easy

Simplify [formula].

Example 3 easy

Simplify [formula].

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