ACT Preparation / Unit 9 ACT 0805 worked example, 60 to 90 seconds
Solving an Equation With Fractions
The idea
To solve an equation with fractions, work in four steps. First, find the least common denominator of every fraction in it. Second, multiply every term on both sides by that LCD, which clears the fractions. Third, solve the resulting equation. Fourth, if a variable appeared in a denominator, reject any answer that makes that denominator zero, and check the rest in the original.
In practice
Worked example: x/3 + x/4 = 7. Step one: the LCD is 12. Step two: 4x + 3x = 84. Step three: 7x = 84, so x = 12. Check: 12/3 + 12/4 = 4 + 3 = 7. Second: 2/(x − 1) = 6/(x + 3). Cross-multiplying gives 2(x + 3) = 6(x − 1), so 2x + 6 = 6x − 6, and x = 3, which makes neither denominator zero.
Where people slip
Multiply every term, including terms with no fraction: in x/2 + 3 = 5, the 3 becomes 6 and the 5 becomes 10, and the solution is x = 4.
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