Question

what is the sum? \\(\frac{x + 2}{14x}+\frac{7}{4x}\\) options: \\(\frac{2x + 53}{28x^2}\\), \\(\frac{2x + 45}{28x}\\), \\(\frac{2x + 53}{28x}\\), \\(\frac{2x + 45}{28x^2}\\)

Explanation:

Step1: Find common denominator

The denominators are $14x$ and $4x$. The least common denominator is $28x$.

Step2: Rewrite fractions with LCD

$$\frac{x+2}{14x} = \frac{2(x+2)}{28x}, \quad \frac{7}{4x} = \frac{49}{28x}$$

Step3: Combine numerators

$$\frac{2(x+2) + 49}{28x}$$

Step4: Simplify numerator

$$\frac{2x + 4 + 49}{28x} = \frac{2x + 53}{28x}$$

Answer:

$\frac{2x+53}{28x}$