\begin{tabular}{l} Find the third proportion of each \\ \( \begin{array}{ll}{[1] 6,12} & {[2] \mathrm{x}^{2},-5 \mathrm{x}}\end{array} \) \\ \hline\end{tabular}

Simplify the following: (1) \( \frac{x-1}{x^{2}+3 x+2} \div\left[\frac{x-3}{x+1}-\frac{x-4}{x+2}\right] \) (2) \( \frac{\frac{6 x+5}{x-5}-1}{\frac{3 x+20}{x-5}+2} \) (3) \( \frac{a^{2}+\left(1-a^{2}\right)}{(1+a) a} \times \frac{(1+a) a}{a^{2}-\left(1-a^{2}\right)} \)

\( x + 5 y \)

Simplify. \( 6 v+3 v \)

Utiliza logaritmos para resolver: \( 5^{x} = 125 \).

Simplify the following: (1) \( \frac{x-1}{x^{2}+3 x+2} \div\left[\frac{x-3}{x+1}-\frac{x-4}{x+2}\right] \) (2) \( \frac{\frac{6 x+5}{x-5}}{\frac{3 x+20}{x-5}+2} \) (3) \( \frac{a^{2}+\left(1-a^{2}\right)}{(1+a) a} \times \frac{(1+a) a}{a^{2}-\left(1-a^{2}\right)} \)