$\frac{1}{x} (x + 1) + \frac{1}{x + 1} (x + 2) = \frac{1}{12}$

Answer

$x_{1} = - \frac{47}{46} - \frac{1105}{46} x_{2} = - \frac{47}{46} + \frac{1105}{46}$

Explanation

\frac{1}{x} (x + 1) + \frac{1}{x + 1} (x + 2) x (x + 1) \cdot 12 \cdot \frac{1}{x} (x + 1) + x (x + 1) \cdot 12 \frac{1}{x + 1} (x + 2) 12 x^{2} + 24 x + 12 + 12 x^{2} + 24 x 24 x^{2} + 48 x + 12 24 x^{2} + 48 x + 12 - x^{2} - x 23 x^{2} + 47 x + 12 = \frac{1}{12} = x (x + 1) \cdot 12 \cdot \frac{1}{12} = x^{2} + x = x^{2} + x = 0 = 0 multiply ALL terms by x (x + 1) \cdot 12 . cancel out the denominators simplify left side move all terms to the left hand side simplify left side

$23 x^{2} + 47 x + 12 = 0$ is a quadratic equation.

You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.

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x1​(x+1)+x+11​(x+2)=121​

x1​=−4647​−461105​​​x2​=−4647​+461105​​​

$\frac{1}{x} (x + 1) + \frac{1}{x + 1} (x + 2) = \frac{1}{12}$

$x_{1} = - \frac{47}{46} - \frac{1105}{46} x_{2} = - \frac{47}{46} + \frac{1105}{46}$