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Chapter 4: Problem 136

Will help you prepare for the material covered in the next section. Solve: \(\frac{x+2}{4 x+3}=\frac{1}{x}\)

Short Answer

Expert verified
The solutions to the equation are \(x = 3\) and \(x = -1\).

Step by step solution

01

Identifying the least common multiple (LCM)

First, identify the least common multiple of the denominators, which in this case is \(4x^2+3x\).
02

Multiplying both sides by the LCM

Multiply both sides of the equation by the LCM to get \(x^2 + 2x = 4x + 3\).
03

Simplify the Equation

Rearrange the equation by subtracting \(2x\) and \(3\) from both sides to get \(x^2 - 2x - 3 = 0\).
04

Factoring the Equation

Factor this quadratic equation to get \((x - 3)(x + 1) = 0\).
05

Solve for \(x\)

Set each factor equal to zero and solve for \(x\). This results in two solutions: \(x = 3\) and \(x = -1\).

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