Evaluate
\frac{3y^{2}-5x}{30xy}
Factor
\frac{\frac{3y^{2}}{x}-5}{30y}
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\frac{y}{10x}-\frac{1}{6y}
Cancel out x in both numerator and denominator.
\frac{y\times 3y}{30xy}-\frac{5x}{30xy}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10x and 6y is 30xy. Multiply \frac{y}{10x} times \frac{3y}{3y}. Multiply \frac{1}{6y} times \frac{5x}{5x}.
\frac{y\times 3y-5x}{30xy}
Since \frac{y\times 3y}{30xy} and \frac{5x}{30xy} have the same denominator, subtract them by subtracting their numerators.
\frac{3y^{2}-5x}{30xy}
Do the multiplications in y\times 3y-5x.
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}