Solve 2/3x-3/2xy+8/5xy-5/6x

$$\frac { 2 } { 3 x } - \frac { 3 } { 2 x y } + \frac { 8 } { 5 x y } - \frac { 5 } { 6 x }$$

Evaluate

$$\frac{3-5y}{30xy}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 2xy is 6xy. Multiply \frac{2}{3x} times \frac{2y}{2y}. Multiply \frac{3}{2xy} times \frac{3}{3}.

$$\frac{2\times 2y}{6xy}-\frac{3\times 3}{6xy}+\frac{8}{5xy}-\frac{5}{6x}$$

Since \frac{2\times 2y}{6xy} and \frac{3\times 3}{6xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2y-3\times 3}{6xy}+\frac{8}{5xy}-\frac{5}{6x}$$

Do the multiplications in 2\times 2y-3\times 3.

$$\frac{4y-9}{6xy}+\frac{8}{5xy}-\frac{5}{6x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6xy and 5xy is 30xy. Multiply \frac{4y-9}{6xy} times \frac{5}{5}. Multiply \frac{8}{5xy} times \frac{6}{6}.

$$\frac{5\left(4y-9\right)}{30xy}+\frac{8\times 6}{30xy}-\frac{5}{6x}$$

Since \frac{5\left(4y-9\right)}{30xy} and \frac{8\times 6}{30xy} have the same denominator, add them by adding their numerators.

$$\frac{5\left(4y-9\right)+8\times 6}{30xy}-\frac{5}{6x}$$

Do the multiplications in 5\left(4y-9\right)+8\times 6.

$$\frac{20y-45+48}{30xy}-\frac{5}{6x}$$

Combine like terms in 20y-45+48.

$$\frac{20y+3}{30xy}-\frac{5}{6x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 30xy and 6x is 30xy. Multiply \frac{5}{6x} times \frac{5y}{5y}.

$$\frac{20y+3}{30xy}-\frac{5\times 5y}{30xy}$$

Since \frac{20y+3}{30xy} and \frac{5\times 5y}{30xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20y+3-5\times 5y}{30xy}$$

Do the multiplications in 20y+3-5\times 5y.

$$\frac{20y+3-25y}{30xy}$$

Combine like terms in 20y+3-25y.

$$\frac{-5y+3}{30xy}$$

Factor

$$\frac{3-5y}{30xy}$$