Simplify the expression \( \frac{2}{x^{2}}+\frac{3}{x^{2}+x} \) and give your answer in the form of \( \frac{f(x)}{g(x)} \). Your answer for the function \( f(x) \) is: Your answer for the function \( g(x) \) is:

To simplify the expression \( \frac{2}{x^{2}}+\frac{3}{x^{2}+x} \), we first need a common denominator. The second term can be factored: \( x^{2} + x = x(x + 1) \). The common denominator for both fractions is \( x^{2}(x + 1) \). Now we rewrite each term with the common denominator: \[ \frac{2}{x^{2}} = \frac{2(x + 1)}{x^{2}(x + 1)} = \frac{2x + 2}{x^{2}(x + 1)} \] \[ \frac{3}{x^{2} + x} = \frac{3}{x(x + 1)} = \frac{3x}{x^{2}(x + 1)} \] Now combine both fractions: \[ \frac{2x + 2 + 3x}{x^{2}(x + 1)} = \frac{5x + 2}{x^{2}(x + 1)} \] So we reach the simplified expression: \(\frac{5x + 2}{x^{2}(x + 1)}\) Thus, for the function \( f(x) \): \( 5x + 2 \) And for the function \( g(x) \): \( x^{2}(x + 1) \)