Question

what is the sum?
\\(\frac{3}{x} + \frac{4}{x^2}\\)
options:
\\(\frac{3x + 4}{x^3}\\)
\\(\frac{7}{x}\\)
\\(\frac{3x + 4}{x^2}\\)
\\(\frac{7}{x + x^2}\\)

Explanation:

Step1: Find a common denominator

The denominators are $x$ and $x^2$. The least common denominator (LCD) is $x^2$.

Step2: Rewrite the first fraction

Rewrite $\frac{3}{x}$ with the LCD $x^2$. Multiply the numerator and denominator by $x$: $\frac{3\times x}{x\times x}=\frac{3x}{x^2}$.

Step3: Add the fractions

Now we have $\frac{3x}{x^2}+\frac{4}{x^2}$. Since the denominators are the same, we add the numerators: $\frac{3x + 4}{x^2}$.

Answer:

$\frac{3x + 4}{x^2}$ (corresponding to the option $\frac{3x+4}{x^2}$)