Evaluate
x_{3}-\frac{1}{x_{2}}
Expand
x_{3}-\frac{1}{x_{2}}
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\frac{x_{1}x_{2}x_{3}-x_{1}}{1-\left(-x_{1}\right)x_{2}-1}
To find the opposite of \left(-x_{1}\right)x_{2}+1, find the opposite of each term.
\frac{x_{1}x_{2}x_{3}-x_{1}}{1+x_{1}x_{2}-1}
Multiply -1 and -1 to get 1.
\frac{x_{1}x_{2}x_{3}-x_{1}}{x_{1}x_{2}}
Subtract 1 from 1 to get 0.
\frac{x_{1}\left(x_{2}x_{3}-1\right)}{x_{1}x_{2}}
Factor the expressions that are not already factored.
\frac{x_{2}x_{3}-1}{x_{2}}
Cancel out x_{1} in both numerator and denominator.
\frac{x_{1}x_{2}x_{3}-x_{1}}{1-\left(-x_{1}\right)x_{2}-1}
To find the opposite of \left(-x_{1}\right)x_{2}+1, find the opposite of each term.
\frac{x_{1}x_{2}x_{3}-x_{1}}{1+x_{1}x_{2}-1}
Multiply -1 and -1 to get 1.
\frac{x_{1}x_{2}x_{3}-x_{1}}{x_{1}x_{2}}
Subtract 1 from 1 to get 0.
\frac{x_{1}\left(x_{2}x_{3}-1\right)}{x_{1}x_{2}}
Factor the expressions that are not already factored.
\frac{x_{2}x_{3}-1}{x_{2}}
Cancel out x_{1} in both numerator and denominator.
Examples
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{ 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}