Solving Rational Equations Math Example 4

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Example 4

medium
Solve 2x−1=4x+3\frac{2}{x-1} = \frac{4}{x+3}.

Solution

  1. 1
    Cross-multiply: 2(x+3)=4(x−1)2(x+3) = 4(x-1), so 2x+6=4x−42x + 6 = 4x - 4.
  2. 2
    10=2x10 = 2x, x=5x = 5. Check: 24=48=12\frac{2}{4} = \frac{4}{8} = \frac{1}{2} ✓

Answer

x=5x = 5
When a rational equation has one fraction on each side, cross-multiplication is the fastest approach. It's equivalent to multiplying both sides by both denominators.

About Solving Rational Equations

Solving equations that contain rational expressions by multiplying every term by the LCD to clear all denominators, solving the resulting polynomial equation, and checking for extraneous solutions.

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More Solving Rational Equations Examples

Example 1 medium

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Example 2 hard

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Example 3 easy

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