\[ \frac{10 x+6}{x-4}+\frac{5 x}{4-x} \] 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:

To simplify the expression \(\frac{10 x+6}{x-4}+\frac{5 x}{4-x}\), we first notice that \(4 - x\) is the same as \(-(x - 4)\). Therefore, we can rewrite the second fraction: \[ \frac{5x}{4-x} = \frac{5x}{-(x-4)} = -\frac{5x}{x-4} \] Now rewriting the entire expression, we have: \[ \frac{10 x + 6}{x - 4} - \frac{5 x}{x - 4} = \frac{(10x + 6 - 5x)}{x - 4} = \frac{5x + 6}{x - 4} \] The numerator is \(5x + 6\) and the denominator is \(x - 4\). So the final answer is: Numerator: \(5x + 6\) Denominator: \(x - 4\)