Question

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

Explanation:

Step1: Find common denominator

The common denominator of $\frac{3}{x}$ and $\frac{4}{x^2}$ is $x^2$.

Step2: Rewrite first fraction

Multiply numerator and denominator of $\frac{3}{x}$ by $x$:
$\frac{3}{x} = \frac{3 \times x}{x \times x} = \frac{3x}{x^2}$

Step3: Add the fractions

Add the numerators over the common denominator:
$\frac{3x}{x^2} + \frac{4}{x^2} = \frac{3x + 4}{x^2}$

Answer:

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