Evaluate
\frac{4x^{2}-5x-4}{x\left(1-x\right)\left(x-2\right)}
Differentiate w.r.t. x
\frac{8-24x+5x^{2}+10x^{3}-4x^{4}}{\left(1-x\right)\left(x-1\right)\left(x\left(x-2\right)\right)^{2}}
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Quiz
Polynomial
5 problems similar to:
\frac { 2 } { x } + \frac { 5 } { 1 - x } - \frac { 1 } { x - 2 }
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\frac{2\left(-x+1\right)}{x\left(-x+1\right)}+\frac{5x}{x\left(-x+1\right)}-\frac{1}{x-2}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 1-x is x\left(-x+1\right). Multiply \frac{2}{x} times \frac{-x+1}{-x+1}. Multiply \frac{5}{1-x} times \frac{x}{x}.
\frac{2\left(-x+1\right)+5x}{x\left(-x+1\right)}-\frac{1}{x-2}
Since \frac{2\left(-x+1\right)}{x\left(-x+1\right)} and \frac{5x}{x\left(-x+1\right)} have the same denominator, add them by adding their numerators.
\frac{-2x+2+5x}{x\left(-x+1\right)}-\frac{1}{x-2}
Do the multiplications in 2\left(-x+1\right)+5x.
\frac{3x+2}{x\left(-x+1\right)}-\frac{1}{x-2}
Combine like terms in -2x+2+5x.
\frac{\left(3x+2\right)\left(x-2\right)}{x\left(x-2\right)\left(-x+1\right)}-\frac{x\left(-x+1\right)}{x\left(x-2\right)\left(-x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(-x+1\right) and x-2 is x\left(x-2\right)\left(-x+1\right). Multiply \frac{3x+2}{x\left(-x+1\right)} times \frac{x-2}{x-2}. Multiply \frac{1}{x-2} times \frac{x\left(-x+1\right)}{x\left(-x+1\right)}.
\frac{\left(3x+2\right)\left(x-2\right)-x\left(-x+1\right)}{x\left(x-2\right)\left(-x+1\right)}
Since \frac{\left(3x+2\right)\left(x-2\right)}{x\left(x-2\right)\left(-x+1\right)} and \frac{x\left(-x+1\right)}{x\left(x-2\right)\left(-x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-6x+2x-4+x^{2}-x}{x\left(x-2\right)\left(-x+1\right)}
Do the multiplications in \left(3x+2\right)\left(x-2\right)-x\left(-x+1\right).
\frac{4x^{2}-5x-4}{x\left(x-2\right)\left(-x+1\right)}
Combine like terms in 3x^{2}-6x+2x-4+x^{2}-x.
\frac{4x^{2}-5x-4}{-x^{3}+3x^{2}-2x}
Expand x\left(x-2\right)\left(-x+1\right).
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}