How do you simplify $2 x + \frac{3}{x^{2} - 9} + \frac{x}{x - 3}$ $2x+3/(x^2-9) + x/(x-3)$ ?

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How do you simplify $2 x + \frac{3}{x^{2} - 9} + \frac{x}{x - 3}$ $2x+3/(x^2-9) + x/(x-3)$ ?

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Answer 1 · 2018-01-11T11:46:22

$\frac{x^{2} + 3 x + 3}{(x - 3) (x + 3)}$ $(x^2+3x+3)/((x-3)(x+3))$

Explanation:

$before adding the fractions we require them to have$ $"before adding the fractions we require them to have"$
$a common denominator$ $"a "color(blue)"common denominator"$

$factorise the denominator x^{2} - 9$ $"factorise the denominator "x^2-9$

$x^{2} - 9 = (x - 3) (x + 3) \leftarrow difference of squares$ $x^2-9=(x-3)(x+3)larrcolor(blue)"difference of squares"$

$multiply numerator/denominator of \frac{x}{x - 3} by (x + 3)$ $"multiply numerator/denominator of"x/(x-3)" by "(x+3)$

$= \frac{3}{(x - 3) (x + 3)} + \frac{x (x + 3)}{(x - 3) (x + 3)}$ $=3/((x-3)(x+3))+(x(x+3))/((x-3)(x+3))$

$add the numerators leaving the denominator$ $"add the numerators leaving the denominator"$

$= \frac{3 + x^{2} + 3 x}{(x - 3) (x + 3)} = \frac{x^{2} + 3 x + 3}{(x - 3) (x + 3)}$ $=(3+x^2+3x)/((x-3)(x+3))=(x^2+3x+3)/((x-3)(x+3))$

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How do you simplify $2 x + \frac{3}{x^{2} - 9} + \frac{x}{x - 3}$ $2x+3/(x^2-9) + x/(x-3)$ ?

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