find the sum:\n$\frac{6}{x - 4}+\frac{5}{x}$\n$\frac{11}{2x - 4}$\n$\frac{11x - 24}{x^{2}-4x}$\n$\frac{11x…
find the sum:\n$\frac{6}{x - 4}+\frac{5}{x}$\n$\frac{11}{2x - 4}$\n$\frac{11x - 24}{x^{2}-4x}$\n$\frac{11x - 20}{x^{2}-4x}$
Answer
Explanation:
Step1: Find common denominator
The common denominator of $x - 4$ and $x$ is $x(x - 4)=x^{2}-4x$.
Step2: Rewrite fractions with common denominator
$\frac{6}{x - 4}\times\frac{x}{x}=\frac{6x}{x^{2}-4x}$ and $\frac{5}{x}\times\frac{x - 4}{x - 4}=\frac{5(x - 4)}{x^{2}-4x}=\frac{5x-20}{x^{2}-4x}$.
Step3: Add the fractions
$\frac{6x}{x^{2}-4x}+\frac{5x - 20}{x^{2}-4x}=\frac{6x+(5x - 20)}{x^{2}-4x}=\frac{6x + 5x-20}{x^{2}-4x}=\frac{11x-20}{x^{2}-4x}$.
Answer:
$\frac{11x - 20}{x^{2}-4x}$