1. The problem is to simplify or analyze the expression $\frac{3\ln x + 7}{\sin^2 x}$. 2. The expression is a fraction where the numerator is $3\ln x + 7$ and the denominator is $\sin^2 x$. 3. There is no direct simplification between numerator and denominator since $\ln x$ and $\sin x$ are different functions. 4. Important rules: - $\ln x$ is the natural logarithm function, defined for $x > 0$. - $\sin^2 x$ means $(\sin x)^2$, the square of the sine function. - The expression is defined only where $x > 0$ and $\sin x \neq 0$ to avoid division by zero. 5. Since no further simplification is possible, the expression remains as is: $$\frac{3\ln x + 7}{\sin^2 x}$$ 6. This expression can be graphed as a function of $x$ for $x > 0$ excluding points where $\sin x = 0$.