Evaluate
\frac{9y}{2}-2x
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\frac{9y}{2}-2x
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\frac{\frac{1}{6}xy\left(4x-9y\right)}{-\frac{1}{3}xy}
Factor the expressions that are not already factored.
\frac{\frac{1}{6}\left(4x-9y\right)}{-\frac{1}{3}}
Cancel out xy in both numerator and denominator.
\frac{\frac{2}{3}x-\frac{3}{2}y}{-\frac{1}{3}}
Expand the expression.
\frac{\left(\frac{2}{3}x-\frac{3}{2}y\right)\times 3}{-1}
Divide \frac{2}{3}x-\frac{3}{2}y by -\frac{1}{3} by multiplying \frac{2}{3}x-\frac{3}{2}y by the reciprocal of -\frac{1}{3}.
-\left(\frac{2}{3}x-\frac{3}{2}y\right)\times 3
Anything divided by -1 gives its opposite.
-\left(2x-\frac{9}{2}y\right)
Use the distributive property to multiply \frac{2}{3}x-\frac{3}{2}y by 3.
-2x+\frac{9}{2}y
To find the opposite of 2x-\frac{9}{2}y, find the opposite of each term.
\frac{\frac{1}{6}xy\left(4x-9y\right)}{-\frac{1}{3}xy}
Factor the expressions that are not already factored.
\frac{\frac{1}{6}\left(4x-9y\right)}{-\frac{1}{3}}
Cancel out xy in both numerator and denominator.
\frac{\frac{2}{3}x-\frac{3}{2}y}{-\frac{1}{3}}
Expand the expression.
\frac{\left(\frac{2}{3}x-\frac{3}{2}y\right)\times 3}{-1}
Divide \frac{2}{3}x-\frac{3}{2}y by -\frac{1}{3} by multiplying \frac{2}{3}x-\frac{3}{2}y by the reciprocal of -\frac{1}{3}.
-\left(\frac{2}{3}x-\frac{3}{2}y\right)\times 3
Anything divided by -1 gives its opposite.
-\left(2x-\frac{9}{2}y\right)
Use the distributive property to multiply \frac{2}{3}x-\frac{3}{2}y by 3.
-2x+\frac{9}{2}y
To find the opposite of 2x-\frac{9}{2}y, find the opposite of each term.
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}