Evaluate
\frac{5x}{12}-\frac{5y}{6}-\frac{1}{3}
Expand
\frac{5x}{12}-\frac{5y}{6}-\frac{1}{3}
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\frac{1}{3}\times 2x+\frac{1}{3}\left(-1\right)y+\frac{1}{3}\left(-1\right)-\frac{1}{4}\left(x+2y\right)
Use the distributive property to multiply \frac{1}{3} by 2x-y-1.
\frac{2}{3}x+\frac{1}{3}\left(-1\right)y+\frac{1}{3}\left(-1\right)-\frac{1}{4}\left(x+2y\right)
Multiply \frac{1}{3} and 2 to get \frac{2}{3}.
\frac{2}{3}x-\frac{1}{3}y+\frac{1}{3}\left(-1\right)-\frac{1}{4}\left(x+2y\right)
Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}\left(x+2y\right)
Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}x-\frac{1}{4}\times 2y
Use the distributive property to multiply -\frac{1}{4} by x+2y.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}x+\frac{-2}{4}y
Express -\frac{1}{4}\times 2 as a single fraction.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}x-\frac{1}{2}y
Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.
\frac{5}{12}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{2}y
Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.
\frac{5}{12}x-\frac{5}{6}y-\frac{1}{3}
Combine -\frac{1}{3}y and -\frac{1}{2}y to get -\frac{5}{6}y.
\frac{1}{3}\times 2x+\frac{1}{3}\left(-1\right)y+\frac{1}{3}\left(-1\right)-\frac{1}{4}\left(x+2y\right)
Use the distributive property to multiply \frac{1}{3} by 2x-y-1.
\frac{2}{3}x+\frac{1}{3}\left(-1\right)y+\frac{1}{3}\left(-1\right)-\frac{1}{4}\left(x+2y\right)
Multiply \frac{1}{3} and 2 to get \frac{2}{3}.
\frac{2}{3}x-\frac{1}{3}y+\frac{1}{3}\left(-1\right)-\frac{1}{4}\left(x+2y\right)
Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}\left(x+2y\right)
Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}x-\frac{1}{4}\times 2y
Use the distributive property to multiply -\frac{1}{4} by x+2y.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}x+\frac{-2}{4}y
Express -\frac{1}{4}\times 2 as a single fraction.
\frac{2}{3}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{4}x-\frac{1}{2}y
Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.
\frac{5}{12}x-\frac{1}{3}y-\frac{1}{3}-\frac{1}{2}y
Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.
\frac{5}{12}x-\frac{5}{6}y-\frac{1}{3}
Combine -\frac{1}{3}y and -\frac{1}{2}y to get -\frac{5}{6}y.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}