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What is one possible solution to the equation
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5 or 7
Students should look for the best solution methods for solving rational equations before they begin. Looking for structure and common denominators will prove very useful at the onset, and will help prevent complex computations that do not lead to a solution.
In this problem, multiplying both sides of the equation by the common denominator yields
Multiplication and simplification then yields or Factoring the quadratic gives so the solutions occur at and both of which should be checked in the original equation to ensure that they are not extraneous. In this case, both values are solutions.
Students must solve a rational equation in one variable.