\[ \frac{10 x+6}{x-4}+\frac{5 x}{4-x} \] Enter the numerator and denominator separately in the boxes below. If the denominator is 1 , enter the number 1. Do not leave either box blank. Make sure that the coefficient on \( x \) is positive. Answer:

The first step is to rewrite the second fraction with a common denominator. Notice that \[ 4-x = -(x-4). \] So, we have \[ \frac{5x}{4-x} = \frac{5x}{-(x-4)} = -\frac{5x}{x-4}. \] Now, rewriting the original expression gives \[ \frac{10x+6}{x-4}+\frac{5x}{4-x} = \frac{10x+6}{x-4} - \frac{5x}{x-4}. \] Since the fractions now have the common denominator \(x-4\), we combine the numerators: \[ \frac{10x+6-5x}{x-4} = \frac{5x+6}{x-4}. \] Thus, the simplified expression is \[ \frac{5x+6}{x-4}. \] Numerator: \(5x+6\) Denominator: \(x-4\)