Evaluate
\frac{1}{4}-\frac{1}{2y}
Expand
\frac{1}{4}-\frac{1}{2y}
Share
Copied to clipboard
\frac{y-2}{2x}\times \frac{3x^{2}-x}{6xy-2y}
Combine 3x and -x to get 2x.
\frac{y-2}{2x}\times \frac{x\left(3x-1\right)}{2y\left(3x-1\right)}
Factor the expressions that are not already factored in \frac{3x^{2}-x}{6xy-2y}.
\frac{y-2}{2x}\times \frac{x}{2y}
Cancel out 3x-1 in both numerator and denominator.
\frac{\left(y-2\right)x}{2x\times 2y}
Multiply \frac{y-2}{2x} times \frac{x}{2y} by multiplying numerator times numerator and denominator times denominator.
\frac{y-2}{2\times 2y}
Cancel out x in both numerator and denominator.
\frac{y-2}{4y}
Multiply 2 and 2 to get 4.
\frac{y-2}{2x}\times \frac{3x^{2}-x}{6xy-2y}
Combine 3x and -x to get 2x.
\frac{y-2}{2x}\times \frac{x\left(3x-1\right)}{2y\left(3x-1\right)}
Factor the expressions that are not already factored in \frac{3x^{2}-x}{6xy-2y}.
\frac{y-2}{2x}\times \frac{x}{2y}
Cancel out 3x-1 in both numerator and denominator.
\frac{\left(y-2\right)x}{2x\times 2y}
Multiply \frac{y-2}{2x} times \frac{x}{2y} by multiplying numerator times numerator and denominator times denominator.
\frac{y-2}{2\times 2y}
Cancel out x in both numerator and denominator.
\frac{y-2}{4y}
Multiply 2 and 2 to get 4.
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}