Evaluate
\frac{4x^{3}+y^{2}}{8xy}
Factor
\frac{4x^{3}+y^{2}}{8xy}
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\frac{x^{2}\times 4x}{8xy}+\frac{yy}{8xy}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2y and 8x is 8xy. Multiply \frac{x^{2}}{2y} times \frac{4x}{4x}. Multiply \frac{y}{8x} times \frac{y}{y}.
\frac{x^{2}\times 4x+yy}{8xy}
Since \frac{x^{2}\times 4x}{8xy} and \frac{yy}{8xy} have the same denominator, add them by adding their numerators.
\frac{4x^{3}+y^{2}}{8xy}
Do the multiplications in x^{2}\times 4x+yy.
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}