Solve 5x+3y/2x^2y-3x+4y/xy^2

$$\frac { 5 x + 3 y } { 2 x ^ { 2 } y } - \frac { 3 x + 4 y } { x y ^ { 2 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x^{2}y and xy^{2} is 2x^{2}y^{2}. Multiply \frac{5x+3y}{2x^{2}y} times \frac{y}{y}. Multiply \frac{3x+4y}{xy^{2}} times \frac{2x}{2x}.

$$\frac{\left(5x+3y\right)y}{2x^{2}y^{2}}-\frac{\left(3x+4y\right)\times 2x}{2x^{2}y^{2}}$$

Since \frac{\left(5x+3y\right)y}{2x^{2}y^{2}} and \frac{\left(3x+4y\right)\times 2x}{2x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x+3y\right)y-\left(3x+4y\right)\times 2x}{2x^{2}y^{2}}$$

Do the multiplications in \left(5x+3y\right)y-\left(3x+4y\right)\times 2x.

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

Combine like terms in 5xy+3y^{2}-6x^{2}-8yx.

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

Expand

$$\frac{3\left(y^{2}-xy-2x^{2}\right)}{2\left(xy\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x^{2}y and xy^{2} is 2x^{2}y^{2}. Multiply \frac{5x+3y}{2x^{2}y} times \frac{y}{y}. Multiply \frac{3x+4y}{xy^{2}} times \frac{2x}{2x}.

$$\frac{\left(5x+3y\right)y}{2x^{2}y^{2}}-\frac{\left(3x+4y\right)\times 2x}{2x^{2}y^{2}}$$

Since \frac{\left(5x+3y\right)y}{2x^{2}y^{2}} and \frac{\left(3x+4y\right)\times 2x}{2x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x+3y\right)y-\left(3x+4y\right)\times 2x}{2x^{2}y^{2}}$$

Do the multiplications in \left(5x+3y\right)y-\left(3x+4y\right)\times 2x.

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

Combine like terms in 5xy+3y^{2}-6x^{2}-8yx.

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