Question

\frac{u+2}{3u-1}+1=\frac{6-u}{u+1}

Answer 1

Explicación paso a paso:

$\frac{u+2}{3u-1}+1=\frac{6-u}{u+1} \\ \\ \frac{u + 2 + 3u - 1}{3u - 1} = \frac{6 - u}{u + 1} \\ \\ \frac{4u + 1}{3u - 1} = \frac{6 - u}{u + 1} \\ \\ (u + 1)(4u + 1) = (3u - 1)(6 - u) \\ 4u {}^{2} + u + 4u + 1 = 18u - 3u {}^{2} - 6 + u \\ 4u {}^{2} + 5u + 1 = 19u - 3u { }^{2} - 6 \\ 4u {}^{2} + 3u {}^{2} + 5u - 19u = - 6 - 1 \\ 7u {}^{2} - 14u = - 7 \\ 7(u {}^{2} - 2u) = - 7 \\ u {}^{2} - 2u = \frac{ - 7}{7} \\ u {}^{2} - 2u = - 1 \\ u {}^{2} - 2u + 1 = 0$

$u {}^{2} - 2u + 1 = 0 \\ u \: \: \: \: \: \: \: \: \: \: \: \: - 1 \\ u \: \: \: \: \: \: \: \: \: \: \: \: - 1 \\ (u - 1)(u - 1) = 0 \\ \\ u - 1 = 0 \\ u = 1$