Simplify. \( \frac{10-7^{2}}{10^{2}+9^{2}} \)

To simplify the expression \( \frac{10-7^{2}}{10^{2}+9^{2}} \), we start by calculating the values in the numerator and the denominator. First, calculate \( 7^2 \): \[ 7^2 = 49 \] Now substitute this value into the numerator: \[ 10 - 7^2 = 10 - 49 = -39 \] Next, calculate \( 10^2 \) and \( 9^2 \): \[ 10^2 = 100,\quad 9^2 = 81 \] Now substitute these values into the denominator: \[ 10^2 + 9^2 = 100 + 81 = 181 \] Now, we can rewrite our expression with the calculated values: \[ \frac{10-7^{2}}{10^{2}+9^{2}} = \frac{-39}{181} \] Therefore, the simplified form of the expression is: \[ \frac{-39}{181} \]