Evaluate
\frac{m}{2}+\frac{n}{3}
Factor
\frac{3m+2n}{6}
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\frac{1}{2}m-\frac{1}{3}n+\frac{2}{3}n
Combine \frac{3}{4}m and -\frac{1}{4}m to get \frac{1}{2}m.
\frac{1}{2}m+\frac{1}{3}n
Combine -\frac{1}{3}n and \frac{2}{3}n to get \frac{1}{3}n.
\frac{9m-4n-3m+8n}{12}
Factor out \frac{1}{12}.
6m+4n
Consider 9m-4n-3m+8n. Multiply and combine like terms.
2\left(3m+2n\right)
Consider 6m+4n. Factor out 2.
\frac{3m+2n}{6}
Rewrite the complete factored expression.
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}