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\frac{3x\left(x+2y\right)}{3x}-\frac{4y^{2}-2xy}{2y}
Factor the expressions that are not already factored in \frac{3x^{2}+6xy}{3x}.
x+2y-\frac{4y^{2}-2xy}{2y}
Cancel out 3x in both numerator and denominator.
x+2y-\frac{2y\left(-x+2y\right)}{2y}
Factor the expressions that are not already factored in \frac{4y^{2}-2xy}{2y}.
x+2y-\left(-x+2y\right)
Cancel out 2y in both numerator and denominator.
x+2y+x-2y
To find the opposite of -x+2y, find the opposite of each term.
2x+2y-2y
Combine x and x to get 2x.
2x
Combine 2y and -2y to get 0.
\frac{3x\left(x+2y\right)}{3x}-\frac{4y^{2}-2xy}{2y}
Factor the expressions that are not already factored in \frac{3x^{2}+6xy}{3x}.
x+2y-\frac{4y^{2}-2xy}{2y}
Cancel out 3x in both numerator and denominator.
x+2y-\frac{2y\left(-x+2y\right)}{2y}
Factor the expressions that are not already factored in \frac{4y^{2}-2xy}{2y}.
x+2y-\left(-x+2y\right)
Cancel out 2y in both numerator and denominator.
x+2y+x-2y
To find the opposite of -x+2y, find the opposite of each term.
2x+2y-2y
Combine x and x to get 2x.
2x
Combine 2y and -2y to get 0.
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}