Evaluate
\frac{2x^{2}+5xy+6y}{2xy}
Expand
\frac{2x^{2}+5xy+6y}{2xy}
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\frac{3\left(x+3\right)}{3x}+\frac{3y+2x}{2y}
Factor the expressions that are not already factored in \frac{3x+9}{3x}.
\frac{x+3}{x}+\frac{3y+2x}{2y}
Cancel out 3 in both numerator and denominator.
\frac{\left(x+3\right)\times 2y}{2xy}+\frac{\left(3y+2x\right)x}{2xy}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 2y is 2xy. Multiply \frac{x+3}{x} times \frac{2y}{2y}. Multiply \frac{3y+2x}{2y} times \frac{x}{x}.
\frac{\left(x+3\right)\times 2y+\left(3y+2x\right)x}{2xy}
Since \frac{\left(x+3\right)\times 2y}{2xy} and \frac{\left(3y+2x\right)x}{2xy} have the same denominator, add them by adding their numerators.
\frac{2xy+6y+3yx+2x^{2}}{2xy}
Do the multiplications in \left(x+3\right)\times 2y+\left(3y+2x\right)x.
\frac{5xy+6y+2x^{2}}{2xy}
Combine like terms in 2xy+6y+3yx+2x^{2}.
\frac{3\left(x+3\right)}{3x}+\frac{3y+2x}{2y}
Factor the expressions that are not already factored in \frac{3x+9}{3x}.
\frac{x+3}{x}+\frac{3y+2x}{2y}
Cancel out 3 in both numerator and denominator.
\frac{\left(x+3\right)\times 2y}{2xy}+\frac{\left(3y+2x\right)x}{2xy}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 2y is 2xy. Multiply \frac{x+3}{x} times \frac{2y}{2y}. Multiply \frac{3y+2x}{2y} times \frac{x}{x}.
\frac{\left(x+3\right)\times 2y+\left(3y+2x\right)x}{2xy}
Since \frac{\left(x+3\right)\times 2y}{2xy} and \frac{\left(3y+2x\right)x}{2xy} have the same denominator, add them by adding their numerators.
\frac{2xy+6y+3yx+2x^{2}}{2xy}
Do the multiplications in \left(x+3\right)\times 2y+\left(3y+2x\right)x.
\frac{5xy+6y+2x^{2}}{2xy}
Combine like terms in 2xy+6y+3yx+2x^{2}.
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}