The square root of the sum of two consecutive odd integers is \( 6 \sqrt{2} \). Find the larger integer. \( \begin{array}{llll}\text { a. } 34 & \text { b. } 35 & \text { c. } 36 & \text { d. } 37\end{array} \)

If \( \frac{1}{2} x+3=\frac{3}{4}-x \), what is the value of \( x ? \)

\( \frac { 4 x y } { x ^ { 2 } + y ^ { 2 } } \)

a) \( \left(3^{6}\right)^{7} \cdot 3^{2}: 3^{41}-5^{2}= \) c) \( \left[\left(2^{2}\right)^{3}\right]^{3}:\left(2^{3}\right)^{5}= \) e) \( 4^{3} \cdot\left(4^{5}\right)^{4}:\left(4^{3}\right)^{7}-2^{4}= \) g) \( \left[\left(5^{3}\right)^{12}:\left(5^{2}\right)^{17}-25\right]: 5= \) i) \( \left.2^{6}+10 \cdot\left[3 \cdot 3^{3}-\left(3^{4}\right)^{3}: 3^{11}\right)\right]= \)

e) \( \sqrt[2]{2} \cdot \sqrt[2]{18}= \)

Aplica el método de fracciones parciales a la función: \( \frac{x^2 + 2}{(x-1)(x+3)} \)