Question

find the sum: \\(\frac{6}{x - 4} + \frac{5}{x}\\) \\(\circ\\) \\(\frac{11}{2x - 4}\\) \\(\circ\\) \\(\frac{11x - 24}{x^2 - 4x}\\) \\(\circ\\) \\(\frac{11x - 20}{x^2 - 4x}\\) done \\(\checkmark\\)

Explanation:

Step1: Find common denominator

The common denominator of $\frac{6}{x-4}$ and $\frac{5}{x}$ is $x(x-4) = x^2-4x$.

Step2: Rewrite fractions with common denominator

$$\frac{6x}{x(x-4)} + \frac{5(x-4)}{x(x-4)}$$

Step3: Expand numerator terms

$$\frac{6x + 5x - 20}{x^2-4x}$$

Step4: Combine like terms in numerator

$$\frac{(6x+5x) - 20}{x^2-4x} = \frac{11x-20}{x^2-4x}$$

Answer:

$\boldsymbol{\frac{11x-20}{x^2-4x}}$ (corresponding to the third option)