Question

What is the sum? 3/x+4/(x)2

Answer 1

(3/x)+(4/(x^2))

give common denominator:
(3x/(x^2))+(4/(x^2)) = (3x+4)/(x^2)

Answer 2

ANSWER

$\frac{3}{x} + \frac{4}{ {x}^{2} } = \frac{3x + 4}{ {x}^{2} }$

EXPLANATION

We want to add the algebraic fractions,

$\frac{3}{x} + \frac{4}{ {x}^{2} }$

To solve this we need to collect LCM.

The LCM of

$x \: and \: {x}^{2} = {x}^{2}$

We can now rewrite the expression as a sum of two equivalent algebraic fractions with the least common multiple as the denominator.

Thus,

$\frac{3}{x} + \frac{4}{ {x}^{2} } = \frac{3x}{ {x}^{2} } + \frac{4}{ {x}^{2} }$


Since the denominators are the same, we write one of them and add the numerators.

This means that,

$\frac{3}{x} + \frac{4}{ {x}^{2} } = \frac{3x + 4}{ {x}^{2} }$