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