If $\left(\frac{1}{2+3}\right)\left(\frac{1}{3+4}\right)=\frac{1}{x+5}$, the value of $x$ is
(A) 4
(B) 7
(C) 30
(D) 37
(E) 67
Solution 1

Taking reciprocals of both sides,

$$
\begin{aligned}
\left(\frac{1}{2+3}\right)\left(\frac{1}{3+4}\right) & =\frac{1}{x+5} \\
(2+3)(3+4) & =x+5 \\
35 & =x+5 \\
x & =30
\end{aligned}
$$

Solution 2

Simplifying the left side,

$$
\begin{aligned}
\left(\frac{1}{2+3}\right)\left(\frac{1}{3+4}\right) & =\frac{1}{x+5} \\
\left(\frac{1}{5}\right)\left(\frac{1}{7}\right) & =\frac{1}{x+5} \\
\frac{1}{35} & =\frac{1}{x+5}
\end{aligned}
$$

Comparing denominators gives $x+5=35$ or $x=30$.

Answer: (C)