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-\frac{2}{a+1}
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-\frac{2}{a+1}
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\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{a}{a+2}-\frac{1}{a\left(a+2\right)}}
Factor a^{2}+2a.
\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{aa}{a\left(a+2\right)}-\frac{1}{a\left(a+2\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+2 and a\left(a+2\right) is a\left(a+2\right). Multiply \frac{a}{a+2} times \frac{a}{a}.
\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{aa-1}{a\left(a+2\right)}}
Since \frac{aa}{a\left(a+2\right)} and \frac{1}{a\left(a+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{a^{2}-1}{a\left(a+2\right)}}
Do the multiplications in aa-1.
\frac{a}{a+1}-\frac{\left(a-1\right)a\left(a+2\right)}{a\left(a^{2}-1\right)}
Divide \frac{a-1}{a} by \frac{a^{2}-1}{a\left(a+2\right)} by multiplying \frac{a-1}{a} by the reciprocal of \frac{a^{2}-1}{a\left(a+2\right)}.
\frac{a}{a+1}-\frac{\left(a-1\right)\left(a+2\right)}{a^{2}-1}
Cancel out a in both numerator and denominator.
\frac{a}{a+1}-\frac{\left(a-1\right)\left(a+2\right)}{\left(a-1\right)\left(a+1\right)}
Factor the expressions that are not already factored in \frac{\left(a-1\right)\left(a+2\right)}{a^{2}-1}.
\frac{a}{a+1}-\frac{a+2}{a+1}
Cancel out a-1 in both numerator and denominator.
\frac{a-\left(a+2\right)}{a+1}
Since \frac{a}{a+1} and \frac{a+2}{a+1} have the same denominator, subtract them by subtracting their numerators.
\frac{a-a-2}{a+1}
Do the multiplications in a-\left(a+2\right).
\frac{-2}{a+1}
Combine like terms in a-a-2.
\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{a}{a+2}-\frac{1}{a\left(a+2\right)}}
Factor a^{2}+2a.
\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{aa}{a\left(a+2\right)}-\frac{1}{a\left(a+2\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+2 and a\left(a+2\right) is a\left(a+2\right). Multiply \frac{a}{a+2} times \frac{a}{a}.
\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{aa-1}{a\left(a+2\right)}}
Since \frac{aa}{a\left(a+2\right)} and \frac{1}{a\left(a+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{a}{a+1}-\frac{\frac{a-1}{a}}{\frac{a^{2}-1}{a\left(a+2\right)}}
Do the multiplications in aa-1.
\frac{a}{a+1}-\frac{\left(a-1\right)a\left(a+2\right)}{a\left(a^{2}-1\right)}
Divide \frac{a-1}{a} by \frac{a^{2}-1}{a\left(a+2\right)} by multiplying \frac{a-1}{a} by the reciprocal of \frac{a^{2}-1}{a\left(a+2\right)}.
\frac{a}{a+1}-\frac{\left(a-1\right)\left(a+2\right)}{a^{2}-1}
Cancel out a in both numerator and denominator.
\frac{a}{a+1}-\frac{\left(a-1\right)\left(a+2\right)}{\left(a-1\right)\left(a+1\right)}
Factor the expressions that are not already factored in \frac{\left(a-1\right)\left(a+2\right)}{a^{2}-1}.
\frac{a}{a+1}-\frac{a+2}{a+1}
Cancel out a-1 in both numerator and denominator.
\frac{a-\left(a+2\right)}{a+1}
Since \frac{a}{a+1} and \frac{a+2}{a+1} have the same denominator, subtract them by subtracting their numerators.
\frac{a-a-2}{a+1}
Do the multiplications in a-\left(a+2\right).
\frac{-2}{a+1}
Combine like terms in a-a-2.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}