Question

What is the sum? StartFraction x Over x 3 EndFraction StartFraction 3 Over x 3 EndFraction 2 Over x 3 EndFraction.

Answer 1

The sum of the considered expression is evaluated to be $\dfrac{x+6}{x+3}$

How to find the sum of a algebraic fractions?

Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in sum of fractions would give the sum of algebraic fractions.

For example,

$\dfrac{a}b} + \dfrac{c}{d} = \dfrac{a \times d + c \times b}{bd}$

For the considered case, the sum of the given expression is easy to evaluate as the denominators are all same, so their sum will directly apply to their numerators.

The sum is evaluated as follows:

$\dfrac{x}{x+3} + \dfrac{2}{x+3} + \dfrac{2}{x+3} = \dfrac{x + 2 + 3}{x+3} = \dfrac{x + 6}{x+3}$

Thus, the sum of the considered expression is evaluated to be $\dfrac{x+6}{x+3}$

Learn more about sum of algebraic fractions here:

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