What is x/(x+1)+1/((x+1)(x+2)) ?

The solution to x/(x+1)+1/((x+1)(x+2)) is (x+1)/(x+2)

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simplify x/(x+1)+1/((x+1)(x+2))

simplify

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

\frac{x + 1}{x + 2}

Solution steps

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

Least Common Multiplier of

x + 1, (x + 1) (x + 2) : (x + 1) (x + 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

\frac{x ^{2} + 2 x + 1}{( x + 1 ) ( x + 2 )} : \frac{x + 1}{x + 2}

= \frac{x + 1}{x + 2}

x^{2} - 1 x - 12

(4 x^{8} y^{3})^{3}

\frac{1}{x} + \frac{3}{x} - \frac{y}{x}

\frac{tan ( x )}{sec ( x )}

\frac{- 81}{9}

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