ANSWER
[tex] \frac{3}{x} + \frac{4}{ {x}^{2} } = \frac{3x + 4}{ {x}^{2} } [/tex]
EXPLANATION
We want to add the algebraic fractions,
[tex] \frac{3}{x} + \frac{4}{ {x}^{2} } [/tex]
To solve this we need to collect LCM.
The LCM of
[tex]x \: and \: {x}^{2} = {x}^{2} [/tex]
We can now rewrite the expression as a sum of two equivalent algebraic fractions with the least common multiple as the denominator.
Thus,
[tex] \frac{3}{x} + \frac{4}{ {x}^{2} } = \frac{3x}{ {x}^{2} } + \frac{4}{ {x}^{2} } [/tex]
Since the denominators are the same, we write one of them and add the numerators.
This means that,
[tex] \frac{3}{x} + \frac{4}{ {x}^{2} } = \frac{3x + 4}{ {x}^{2} } [/tex]
