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-\frac{2}{c}
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-\frac{2}{c}
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\frac{\left(a+b\right)c}{abc}-\frac{\left(b+c\right)a}{abc}-\frac{c+a}{ca}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of ab and bc is abc. Multiply \frac{a+b}{ab} times \frac{c}{c}. Multiply \frac{b+c}{bc} times \frac{a}{a}.
\frac{\left(a+b\right)c-\left(b+c\right)a}{abc}-\frac{c+a}{ca}
Since \frac{\left(a+b\right)c}{abc} and \frac{\left(b+c\right)a}{abc} have the same denominator, subtract them by subtracting their numerators.
\frac{ac+bc-ba-ca}{abc}-\frac{c+a}{ca}
Do the multiplications in \left(a+b\right)c-\left(b+c\right)a.
\frac{bc-ba}{abc}-\frac{c+a}{ca}
Combine like terms in ac+bc-ba-ca.
\frac{b\left(-a+c\right)}{abc}-\frac{c+a}{ca}
Factor the expressions that are not already factored in \frac{bc-ba}{abc}.
\frac{-a+c}{ac}-\frac{c+a}{ca}
Cancel out b in both numerator and denominator.
\frac{-a+c-\left(c+a\right)}{ac}
Since \frac{-a+c}{ac} and \frac{c+a}{ca} have the same denominator, subtract them by subtracting their numerators.
\frac{-a+c-c-a}{ac}
Do the multiplications in -a+c-\left(c+a\right).
\frac{-2a}{ac}
Combine like terms in -a+c-c-a.
\frac{-2}{c}
Cancel out a in both numerator and denominator.
\frac{\left(a+b\right)c}{abc}-\frac{\left(b+c\right)a}{abc}-\frac{c+a}{ca}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of ab and bc is abc. Multiply \frac{a+b}{ab} times \frac{c}{c}. Multiply \frac{b+c}{bc} times \frac{a}{a}.
\frac{\left(a+b\right)c-\left(b+c\right)a}{abc}-\frac{c+a}{ca}
Since \frac{\left(a+b\right)c}{abc} and \frac{\left(b+c\right)a}{abc} have the same denominator, subtract them by subtracting their numerators.
\frac{ac+bc-ba-ca}{abc}-\frac{c+a}{ca}
Do the multiplications in \left(a+b\right)c-\left(b+c\right)a.
\frac{bc-ba}{abc}-\frac{c+a}{ca}
Combine like terms in ac+bc-ba-ca.
\frac{b\left(-a+c\right)}{abc}-\frac{c+a}{ca}
Factor the expressions that are not already factored in \frac{bc-ba}{abc}.
\frac{-a+c}{ac}-\frac{c+a}{ca}
Cancel out b in both numerator and denominator.
\frac{-a+c-\left(c+a\right)}{ac}
Since \frac{-a+c}{ac} and \frac{c+a}{ca} have the same denominator, subtract them by subtracting their numerators.
\frac{-a+c-c-a}{ac}
Do the multiplications in -a+c-\left(c+a\right).
\frac{-2a}{ac}
Combine like terms in -a+c-c-a.
\frac{-2}{c}
Cancel out a 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}