Question

what is the sum? (\frac{2x}{x^2} + \frac{x - 4}{9x}) options: (\frac{x^2 + 14x}{9x}), (\frac{x^2 + 14x}{9x^2}), (\frac{x^2 - 22x}{9x^2}), (\frac{x^2 - 22x}{9x})

Explanation:

Step1: Find common denominator

The denominators are $x^2$ and $9x$, so the least common denominator is $9x^2$.

Step2: Rewrite fractions with LCD

$$\frac{2x}{x^2} = \frac{2x \cdot 9}{x^2 \cdot 9} = \frac{18x}{9x^2}, \quad \frac{x-4}{9x} = \frac{(x-4) \cdot x}{9x \cdot x} = \frac{x^2 - 4x}{9x^2}$$

Step3: Add the numerators

$$\frac{18x + x^2 - 4x}{9x^2}$$

Step4: Simplify the numerator

$$\frac{x^2 + (18x - 4x)}{9x^2} = \frac{x^2 + 14x}{9x^2}$$

Answer:

$\frac{x^2 + 14x}{9x^2}$