$x - \frac{4 x + 3}{x + 5} = \frac{2 x + 27}{x + 5}$

Answer

$x_{1} = - 5 x_{2} = 6$

Explanation

x - \frac{4 x + 3}{x + 5} (x + 5) x - (x + 5) \frac{4 x + 3}{x + 5} x^{2} + 5 x - (4 x + 3) x^{2} + 5 x - 4 x - 3 x^{2} + x - 3 x^{2} + x - 3 - 2 x - 27 x^{2} - x - 30 = \frac{2 x + 27}{x + 5} = (x + 5) \frac{2 x + 27}{x + 5} = 2 x + 27 = 2 x + 27 = 2 x + 27 = 0 = 0 multiply ALL terms by x + 5 . cancel out the denominators simplify left side move all terms to the left hand side simplify left side

$x^{2} - x - 30 = 0$ 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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x−x+54x+3​=x+52x+27​

x1​=−5​x2​=6​

$x - \frac{4 x + 3}{x + 5} = \frac{2 x + 27}{x + 5}$

$x_{1} = - 5 x_{2} = 6$