All of the equations in the previous section could be solved using cross-multiplying to simplify the equation. Not all rational equations will be that simple to solve.

If the equation is not written as a proportion, then you will need to clear out the denominators by multiplying every part of the equation by the least common denominator. The next two examples will demonstrate this.

Example 1

Solve the equation numerator p + 1 denominator p + 2 + numerator 5 denominator p = numerator 2p + 9 denominator p + 2 p + 1 p + 2 + 5 p 2p + 9 p + 2 .

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Check Your Answer

p = -5 or p = 2

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Example 2

Solve the equation numerator 2M + 12 denominator m^2 + 6m plus numerator 2m + 2 denominator m + 6 equals numerator 4m + 2 denominator m + 6 2m + 12 m² + 6m 2m + 2 m + 6 = 4m + 2 m + 6

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Check Your Answer

m = -2 or m = 3

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