Question

(x+2/x+1)^2=x+4/x+2​

Answer 1

Answer:

$x = - \frac{4}{3}$

Step-by-step explanation:

$\frac{ {(x + 2)}^{2} }{(x + 1) {}^{2} } = \frac{x + 4}{x + 2} \\ \\ (1 + \frac{1}{(x + 1)} ) {}^{2} = 1 + \frac{2}{x + 2} \\ \\ 1 + \frac{2}{ {(x + 1)}} + \frac{1}{ {(x + 1)}^{2} } = 1 + \frac{2}{(x + 2)} \\ \\ \frac{1}{(x + 1) {}^{2} } = 2( \frac{1}{x + 2} - \frac{1}{x + 1} ) \\ \\ \frac{1}{ {(x + 1)}^{2} } = - \frac{2}{(x + 1)(x + 2)} \\ \\ if \: \: x \neq - 1 \\ \\ \frac{1}{x + 1} = - \frac{2}{x + 2} \\ \\ x + 2 = - 2x - 2 \\ \\ x = - \frac{4}{3}$

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