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\frac{2}{a}
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\frac{2}{a}
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\frac{\left(a+b\right)c}{abc}+\frac{\left(b-c\right)a}{abc}+\frac{c-a}{ac}
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}{ac}
Since \frac{\left(a+b\right)c}{abc} and \frac{\left(b-c\right)a}{abc} have the same denominator, add them by adding their numerators.
\frac{ac+bc+ba-ca}{abc}+\frac{c-a}{ac}
Do the multiplications in \left(a+b\right)c+\left(b-c\right)a.
\frac{bc+ba}{abc}+\frac{c-a}{ac}
Combine like terms in ac+bc+ba-ca.
\frac{b\left(a+c\right)}{abc}+\frac{c-a}{ac}
Factor the expressions that are not already factored in \frac{bc+ba}{abc}.
\frac{a+c}{ac}+\frac{c-a}{ac}
Cancel out b in both numerator and denominator.
\frac{a+c+c-a}{ac}
Since \frac{a+c}{ac} and \frac{c-a}{ac} have the same denominator, add them by adding their numerators.
\frac{2c}{ac}
Combine like terms in a+c+c-a.
\frac{2}{a}
Cancel out c in both numerator and denominator.
\frac{\left(a+b\right)c}{abc}+\frac{\left(b-c\right)a}{abc}+\frac{c-a}{ac}
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}{ac}
Since \frac{\left(a+b\right)c}{abc} and \frac{\left(b-c\right)a}{abc} have the same denominator, add them by adding their numerators.
\frac{ac+bc+ba-ca}{abc}+\frac{c-a}{ac}
Do the multiplications in \left(a+b\right)c+\left(b-c\right)a.
\frac{bc+ba}{abc}+\frac{c-a}{ac}
Combine like terms in ac+bc+ba-ca.
\frac{b\left(a+c\right)}{abc}+\frac{c-a}{ac}
Factor the expressions that are not already factored in \frac{bc+ba}{abc}.
\frac{a+c}{ac}+\frac{c-a}{ac}
Cancel out b in both numerator and denominator.
\frac{a+c+c-a}{ac}
Since \frac{a+c}{ac} and \frac{c-a}{ac} have the same denominator, add them by adding their numerators.
\frac{2c}{ac}
Combine like terms in a+c+c-a.
\frac{2}{a}
Cancel out c 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}