Evaluate
-\frac{x^{2}+xy+y^{2}}{2x}
Expand
-\frac{x^{2}+xy+y^{2}}{2x}
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\frac{\left(x+y\right)\left(x-2y\right)\left(x-y\right)\left(x^{2}+xy+y^{2}\right)}{2x\left(x+y\right)\left(x-y\right)\left(-x+2y\right)}
Factor the expressions that are not already factored.
\frac{-\left(x+y\right)\left(x-y\right)\left(-x+2y\right)\left(x^{2}+xy+y^{2}\right)}{2x\left(x+y\right)\left(x-y\right)\left(-x+2y\right)}
Extract the negative sign in x-2y.
\frac{-\left(x^{2}+xy+y^{2}\right)}{2x}
Cancel out \left(x+y\right)\left(x-y\right)\left(-x+2y\right) in both numerator and denominator.
\frac{-x^{2}-xy-y^{2}}{2x}
Expand the expression.
\frac{\left(x+y\right)\left(x-2y\right)\left(x-y\right)\left(x^{2}+xy+y^{2}\right)}{2x\left(x+y\right)\left(x-y\right)\left(-x+2y\right)}
Factor the expressions that are not already factored.
\frac{-\left(x+y\right)\left(x-y\right)\left(-x+2y\right)\left(x^{2}+xy+y^{2}\right)}{2x\left(x+y\right)\left(x-y\right)\left(-x+2y\right)}
Extract the negative sign in x-2y.
\frac{-\left(x^{2}+xy+y^{2}\right)}{2x}
Cancel out \left(x+y\right)\left(x-y\right)\left(-x+2y\right) in both numerator and denominator.
\frac{-x^{2}-xy-y^{2}}{2x}
Expand the expression.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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
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