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Advanced Math
/ Nonlinear equations in one variable and systems of equations in two variables
Difficulty: Medium
What is the positive solution to the given equation?
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Explanation
The correct answer is . Multiplying both sides of the given equation by results in . Applying the distributive property of multiplication to the right-hand side of this equation results in . Subtracting from both sides of this equation results in . The right-hand side of this equation can be rewritten by factoring. The two values that multiply to and add to are and . It follows that the equation can be rewritten as . Setting each factor equal to yields two equations: and . Subtracting from both sides of the equation results in . Adding to both sides of the equation results in . Therefore, the positive solution to the given equation is .