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

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Answer 1 · 2017-04-07T13:01:49

$= \frac{4 (x + 1)}{x (x + 2)}$ $= (4(x+1))/(x(x+2))$

In order to simplify two fractions you need to convert both fractions to a common denominator (which in this case is $x (x + 2)$ $x(x+2)$ )

$\frac{x + 2}{x} \times \frac{x + 2}{x + 2} - \frac{x}{x + 2} \times \frac{x}{x}$ $(x+2)/x xx color(red)((x+2)/(x+2)) - x/(x+2) xx color(red)(x/x)$

$= \frac{(x + 2) (x + 2) - x \times x}{x (x + 2)}$ $= ((x+2)(x+2) - x xx x)/(x(x+2)$

$= \frac{x^{2} + 4 x + 4 - x^{2}}{x (x + 2)}$ $= (x^2 +4x +4 -x^2)/(x(x+2)$

$= \frac{4 x + 4}{x (x + 2)}$ $= (4x+4)/(x(x+2)$

$= \frac{4 (x + 1)}{x (x + 2)}$ $= (4(x+1))/(x(x+2))$

NOTE:
Both $\frac{x + 2}{x + 2} and \frac{x}{x}$ $color(red)((x+2)/(x+2)) and color(red)(x/x)$ are equal to $1$ $color(red)(1)$

Multiplying by 1 does not affect the value of an expression, just what it looks like.

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