Solving Rational Equations Math Example 1

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Example 1

medium
Solve 3x+12=5x\frac{3}{x} + \frac{1}{2} = \frac{5}{x}.

Solution

  1. 1
    Step 1: LCD = 2x2x. Multiply every term: 2x⋅3x+2x⋅12=2x⋅5x2x \cdot \frac{3}{x} + 2x \cdot \frac{1}{2} = 2x \cdot \frac{5}{x}.
  2. 2
    Step 2: Simplify: 6+x=106 + x = 10.
  3. 3
    Step 3: Solve: x=4x = 4.
  4. 4
    Check: 34+12=54\frac{3}{4} + \frac{1}{2} = \frac{5}{4} and 54\frac{5}{4} ✓

Answer

x=4x = 4
To solve a rational equation, multiply every term by the LCD to clear all denominators. This converts the rational equation into a simpler polynomial equation.

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.

Learn more about Solving Rational Equations →

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Example 2 hard

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