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\frac{\frac{x}{x}-\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{x-3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{x}{x} and \frac{3}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{\left(x-3\right)x}{x^{2}}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-3}{x} times \frac{x}{x}.
\frac{\frac{\left(x-3\right)x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{\left(x-3\right)x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Do the multiplications in \left(x-3\right)x+2.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x}{x^{2}}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{1}{x} times \frac{x}{x}.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x-2}{x^{2}}}
Since \frac{x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x^{2}-3x+2\right)x^{2}}{x^{2}\left(x-2\right)}
Divide \frac{x^{2}-3x+2}{x^{2}} by \frac{x-2}{x^{2}} by multiplying \frac{x^{2}-3x+2}{x^{2}} by the reciprocal of \frac{x-2}{x^{2}}.
\frac{x^{2}-3x+2}{x-2}
Cancel out x^{2} in both numerator and denominator.
\frac{\left(x-2\right)\left(x-1\right)}{x-2}
Factor the expressions that are not already factored.
x-1
Cancel out x-2 in both numerator and denominator.
\frac{\frac{x}{x}-\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.
\frac{\frac{x-3}{x}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{x}{x} and \frac{3}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{\left(x-3\right)x}{x^{2}}+\frac{2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-3}{x} times \frac{x}{x}.
\frac{\frac{\left(x-3\right)x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Since \frac{\left(x-3\right)x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{1}{x}-\frac{2}{x^{2}}}
Do the multiplications in \left(x-3\right)x+2.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x}{x^{2}}-\frac{2}{x^{2}}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{1}{x} times \frac{x}{x}.
\frac{\frac{x^{2}-3x+2}{x^{2}}}{\frac{x-2}{x^{2}}}
Since \frac{x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{\left(x^{2}-3x+2\right)x^{2}}{x^{2}\left(x-2\right)}
Divide \frac{x^{2}-3x+2}{x^{2}} by \frac{x-2}{x^{2}} by multiplying \frac{x^{2}-3x+2}{x^{2}} by the reciprocal of \frac{x-2}{x^{2}}.
\frac{x^{2}-3x+2}{x-2}
Cancel out x^{2} in both numerator and denominator.
\frac{\left(x-2\right)\left(x-1\right)}{x-2}
Factor the expressions that are not already factored.
x-1
Cancel out x-2 in both numerator and denominator.
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}