Question

what is the sum?
\\(\frac{2}{x^2} + \frac{4}{x^2}\\)
options:
\\(\frac{6}{x^2}\\)
\\(\frac{8}{x^4}\\)
\\(\frac{6}{2x^2}\\)
\\(\frac{8}{x^2}\\)

Explanation:

Step1: Recall the rule for adding fractions with the same denominator.

When adding fractions \(\frac{a}{c} + \frac{b}{c}\), we use the rule \(\frac{a}{c}+\frac{b}{c}=\frac{a + b}{c}\), where \(c
eq0\). In the given problem, the two fractions are \(\frac{2}{x^{2}}\) and \(\frac{4}{x^{2}}\), so they have the same denominator \(x^{2}\).

Step2: Apply the rule to the given fractions.

Using the rule from Step 1, we add the numerators \(2\) and \(4\) while keeping the denominator \(x^{2}\) the same. So, \(\frac{2}{x^{2}}+\frac{4}{x^{2}}=\frac{2 + 4}{x^{2}}\).

Step3: Simplify the numerator.

Calculate \(2+4\), which equals \(6\). So the sum is \(\frac{6}{x^{2}}\).

Answer:

\(\frac{6}{x^{2}}\) (corresponding to the option \(\boldsymbol{\frac{6}{x^{2}}}\))