Solve y-2/3x-x+3x^2-x/6xy-2y

$$\frac{ y-2 }{ 3x-x } + \frac{ 3 { x }^{ 2 } -x }{ 6xy-2y }$$

Evaluate

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

Short Solution Steps

Combine 3x and -x to get 2x.

$$\frac{y-2}{2x}+\frac{3x^{2}-x}{6xy-2y}$$

Factor the expressions that are not already factored in \frac{3x^{2}-x}{6xy-2y}.

$$\frac{y-2}{2x}+\frac{x\left(3x-1\right)}{2y\left(3x-1\right)}$$

Cancel out 3x-1 in both numerator and denominator.

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

Combine 3x and -x to get 2x.

$$\frac{y-2}{2x}+\frac{3x^{2}-x}{6xy-2y}$$

Factor the expressions that are not already factored in \frac{3x^{2}-x}{6xy-2y}.

$$\frac{y-2}{2x}+\frac{x\left(3x-1\right)}{2y\left(3x-1\right)}$$

Cancel out 3x-1 in both numerator and denominator.

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

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

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

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

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

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

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