Evaluate
-8x+12+\frac{8}{x}
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-8x+12+\frac{8}{x}
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\frac{\frac{\left(8x+4\right)\left(x^{2}-2x\right)}{x-1}}{\frac{x^{2}}{1-x}}
Express \left(8x+4\right)\times \frac{x^{2}-2x}{x-1} as a single fraction.
\frac{\left(8x+4\right)\left(x^{2}-2x\right)\left(1-x\right)}{\left(x-1\right)x^{2}}
Divide \frac{\left(8x+4\right)\left(x^{2}-2x\right)}{x-1} by \frac{x^{2}}{1-x} by multiplying \frac{\left(8x+4\right)\left(x^{2}-2x\right)}{x-1} by the reciprocal of \frac{x^{2}}{1-x}.
\frac{-\left(x-1\right)\left(8x+4\right)\left(x^{2}-2x\right)}{\left(x-1\right)x^{2}}
Extract the negative sign in 1-x.
\frac{-\left(8x+4\right)\left(x^{2}-2x\right)}{x^{2}}
Cancel out x-1 in both numerator and denominator.
\frac{-4x\left(x-2\right)\left(2x+1\right)}{x^{2}}
Factor the expressions that are not already factored.
\frac{-4\left(x-2\right)\left(2x+1\right)}{x}
Cancel out x in both numerator and denominator.
\frac{-8x^{2}+12x+8}{x}
Expand the expression.
\frac{\frac{\left(8x+4\right)\left(x^{2}-2x\right)}{x-1}}{\frac{x^{2}}{1-x}}
Express \left(8x+4\right)\times \frac{x^{2}-2x}{x-1} as a single fraction.
\frac{\left(8x+4\right)\left(x^{2}-2x\right)\left(1-x\right)}{\left(x-1\right)x^{2}}
Divide \frac{\left(8x+4\right)\left(x^{2}-2x\right)}{x-1} by \frac{x^{2}}{1-x} by multiplying \frac{\left(8x+4\right)\left(x^{2}-2x\right)}{x-1} by the reciprocal of \frac{x^{2}}{1-x}.
\frac{-\left(x-1\right)\left(8x+4\right)\left(x^{2}-2x\right)}{\left(x-1\right)x^{2}}
Extract the negative sign in 1-x.
\frac{-\left(8x+4\right)\left(x^{2}-2x\right)}{x^{2}}
Cancel out x-1 in both numerator and denominator.
\frac{-4x\left(x-2\right)\left(2x+1\right)}{x^{2}}
Factor the expressions that are not already factored.
\frac{-4\left(x-2\right)\left(2x+1\right)}{x}
Cancel out x in both numerator and denominator.
\frac{-8x^{2}+12x+8}{x}
Expand the expression.
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
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