What is x/(x^2-x-2)+(2+x)/(x-2) ?

The solution to x/(x^2-x-2)+(2+x)/(x-2) is (x^2+4x+2)/((x+1)(x-2))

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simplify x/(x^2-x-2)+(2+x)/(x-2)

simplify

\frac{x}{x ^{2} - x - 2} + \frac{2 + x}{x - 2}

\frac{x ^{2} + 4 x + 2}{( x + 1 ) ( x - 2 )}

Solution steps

\frac{x}{x ^{2} - x - 2} + \frac{2 + x}{x - 2}

Least Common Multiplier of

x^{2} - x - 2, x - 2 : (x + 1) (x - 2)

Adjust Fractions based on the LCM

= \frac{x}{( x + 1 ) ( x - 2 )} + \frac{( 2 + x ) ( x + 1 )}{( x + 1 ) ( x - 2 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{x + ( 2 + x ) ( x + 1 )}{( x + 1 ) ( x - 2 )}

Simplify

x + (2 + x) (x + 1) : x^{2} + 4 x + 2

= \frac{x ^{2} + 4 x + 2}{( x + 1 ) ( x - 2 )}

(4 x^{2} + 1)^{2}

\frac{\frac{6 h - 15}{6}}{\frac{2 h - 5}{5}}

2 x \cdot 5 x

\frac{6 x ^{2} - 14 x}{15 x} + \frac{3 x ^{2} + 17 x}{15 x}

\frac{5}{6} \cdot \frac{3}{4}

What is x/(x^2-x-2)+(2+x)/(x-2) ?
The solution to x/(x^2-x-2)+(2+x)/(x-2) is (x^2+4x+2)/((x+1)(x-2))