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\frac{\left(x+1\right)\left(x+2\right)-x\left(x+1\right)}{2}
Since \frac{\left(x+1\right)\left(x+2\right)}{2} and \frac{x\left(x+1\right)}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+2x+x+2-x^{2}-x}{2}
Do the multiplications in \left(x+1\right)\left(x+2\right)-x\left(x+1\right).
\frac{2x+2}{2}
Combine like terms in x^{2}+2x+x+2-x^{2}-x.
1+x
Divide each term of 2x+2 by 2 to get 1+x.
\frac{\left(x+1\right)\left(x+2\right)-x\left(x+1\right)}{2}
Since \frac{\left(x+1\right)\left(x+2\right)}{2} and \frac{x\left(x+1\right)}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+2x+x+2-x^{2}-x}{2}
Do the multiplications in \left(x+1\right)\left(x+2\right)-x\left(x+1\right).
\frac{2x+2}{2}
Combine like terms in x^{2}+2x+x+2-x^{2}-x.
1+x
Divide each term of 2x+2 by 2 to get 1+x.
Examples
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}