Simplify the expression \( \frac{1}{x+4}-\frac{1}{x+7} \) 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 \( \frac{1}{x+4}-\frac{1}{x+7} \), we need a common denominator. The common denominator is \( (x+4)(x+7) \). Now, rewrite each fraction: \[ \frac{1}{x+4} = \frac{x+7}{(x+4)(x+7)} \] \[ \frac{1}{x+7} = \frac{x+4}{(x+4)(x+7)} \] Now substitute these into the expression: \[ \frac{x+7}{(x+4)(x+7)} - \frac{x+4}{(x+4)(x+7)} = \frac{(x+7) - (x+4)}{(x+4)(x+7)} \] Simplifying the numerator: \[ (x+7) - (x+4) = 7 - 4 = 3 \] So, the expression becomes: \[ \frac{3}{(x+4)(x+7)} \] Thus, in the form of \( \frac{f(x)}{g(x)} \): Your answer for the function \( f(x) \) is: \( 3 \) Your answer for the function \( g(x) \) is: \( (x+4)(x+7) \)