Solve 2x(x-2y)/2xy+(x-2y)/2xy

$$\frac { 2 x ( x - 2 y ) } { 2 x y } + \frac { ( x - 2 y ) } { 2 x y }$$

Evaluate

$$\frac{\left(x-2y\right)\left(2x+1\right)}{2xy}$$

Short Solution Steps

Cancel out 2x in both numerator and denominator.

$$\frac{x-2y}{y}+\frac{x-2y}{2xy}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 2xy is 2xy. Multiply \frac{x-2y}{y} times \frac{2x}{2x}.

$$\frac{\left(x-2y\right)\times 2x}{2xy}+\frac{x-2y}{2xy}$$

Since \frac{\left(x-2y\right)\times 2x}{2xy} and \frac{x-2y}{2xy} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-2y\right)\times 2x+x-2y}{2xy}$$

Do the multiplications in \left(x-2y\right)\times 2x+x-2y.

$$\frac{2x^{2}-4yx+x-2y}{2xy}$$

Expand

$$-\frac{2y-x+4xy-2x^{2}}{2xy}$$

Short Solution Steps

Cancel out 2x in both numerator and denominator.

$$\frac{x-2y}{y}+\frac{x-2y}{2xy}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 2xy is 2xy. Multiply \frac{x-2y}{y} times \frac{2x}{2x}.

$$\frac{\left(x-2y\right)\times 2x}{2xy}+\frac{x-2y}{2xy}$$

Since \frac{\left(x-2y\right)\times 2x}{2xy} and \frac{x-2y}{2xy} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-2y\right)\times 2x+x-2y}{2xy}$$

Do the multiplications in \left(x-2y\right)\times 2x+x-2y.

$$\frac{2x^{2}-4yx+x-2y}{2xy}$$