Evaluate
\frac{x-z}{xz}
Expand
\frac{x-z}{xz}
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\frac{\left(x-y\right)z}{xyz}+\frac{\left(y-z\right)x}{xyz}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of xy and yz is xyz. Multiply \frac{x-y}{xy} times \frac{z}{z}. Multiply \frac{y-z}{yz} times \frac{x}{x}.
\frac{\left(x-y\right)z+\left(y-z\right)x}{xyz}
Since \frac{\left(x-y\right)z}{xyz} and \frac{\left(y-z\right)x}{xyz} have the same denominator, add them by adding their numerators.
\frac{xz-yz+yx-zx}{xyz}
Do the multiplications in \left(x-y\right)z+\left(y-z\right)x.
\frac{-yz+yx}{xyz}
Combine like terms in xz-yz+yx-zx.
\frac{y\left(x-z\right)}{xyz}
Factor the expressions that are not already factored in \frac{-yz+yx}{xyz}.
\frac{x-z}{xz}
Cancel out y in both numerator and denominator.
\frac{\left(x-y\right)z}{xyz}+\frac{\left(y-z\right)x}{xyz}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of xy and yz is xyz. Multiply \frac{x-y}{xy} times \frac{z}{z}. Multiply \frac{y-z}{yz} times \frac{x}{x}.
\frac{\left(x-y\right)z+\left(y-z\right)x}{xyz}
Since \frac{\left(x-y\right)z}{xyz} and \frac{\left(y-z\right)x}{xyz} have the same denominator, add them by adding their numerators.
\frac{xz-yz+yx-zx}{xyz}
Do the multiplications in \left(x-y\right)z+\left(y-z\right)x.
\frac{-yz+yx}{xyz}
Combine like terms in xz-yz+yx-zx.
\frac{y\left(x-z\right)}{xyz}
Factor the expressions that are not already factored in \frac{-yz+yx}{xyz}.
\frac{x-z}{xz}
Cancel out y 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}