Solve x+1/y-x+2/2y/frac{x*y{6}}=?

$$\frac { \frac { x + 1 } { y } - \frac { x + 2 } { 2 y } } { \frac { x \cdot y } { 6 } } = ?$$

Evaluate

$$\frac{3}{y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 2y is 2y. Multiply \frac{x+1}{y} times \frac{2}{2}.

$$\frac{\frac{2\left(x+1\right)}{2y}-\frac{x+2}{2y}}{\frac{xy}{6}}$$

Since \frac{2\left(x+1\right)}{2y} and \frac{x+2}{2y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2\left(x+1\right)-\left(x+2\right)}{2y}}{\frac{xy}{6}}$$

Do the multiplications in 2\left(x+1\right)-\left(x+2\right).

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

Combine like terms in 2x+2-x-2.

$$\frac{\frac{x}{2y}}{\frac{xy}{6}}$$

Divide \frac{x}{2y} by \frac{xy}{6} by multiplying \frac{x}{2y} by the reciprocal of \frac{xy}{6}.

$$\frac{x\times 6}{2yxy}$$

Cancel out 2x in both numerator and denominator.

$$\frac{3}{yy}$$

Multiply y and y to get y^{2}.

$$\frac{3}{y^{2}}$$

Expand

$$\frac{3}{y^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 2y is 2y. Multiply \frac{x+1}{y} times \frac{2}{2}.

$$\frac{\frac{2\left(x+1\right)}{2y}-\frac{x+2}{2y}}{\frac{xy}{6}}$$

Since \frac{2\left(x+1\right)}{2y} and \frac{x+2}{2y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2\left(x+1\right)-\left(x+2\right)}{2y}}{\frac{xy}{6}}$$

Do the multiplications in 2\left(x+1\right)-\left(x+2\right).

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

Combine like terms in 2x+2-x-2.

$$\frac{\frac{x}{2y}}{\frac{xy}{6}}$$

Divide \frac{x}{2y} by \frac{xy}{6} by multiplying \frac{x}{2y} by the reciprocal of \frac{xy}{6}.

$$\frac{x\times 6}{2yxy}$$

Cancel out 2x in both numerator and denominator.

$$\frac{3}{yy}$$

Multiply y and y to get y^{2}.

$$\frac{3}{y^{2}}$$