Subtract. Write the answer in lowest terms. \[ \frac{10}{x+10}-\frac{11}{x} \]

To subtract the fractions, we need a common denominator, which is \(x(x + 10)\). Rewriting each fraction with the common denominator: \[ \frac{10}{x+10} = \frac{10x}{x(x+10)} \] \[ \frac{11}{x} = \frac{11(x + 10)}{x(x+10)} = \frac{11x + 110}{x(x + 10)} \] Now, we can combine the fractions: \[ \frac{10x}{x(x + 10)} - \frac{11x + 110}{x(x + 10)} = \frac{10x - (11x + 110)}{x(x + 10)} \] Simplifying the numerator: \[ 10x - 11x - 110 = -x - 110 \] So the combined fraction is: \[ \frac{-x - 110}{x(x + 10)} \] To express this in lowest terms, we can factor out \( -1 \): \[ \frac{-(x + 110)}{x(x + 10)} \] Thus, the final answer is: \[ \frac{-(x + 110)}{x(x + 10)} \]