Solve 5x+5y/3x^2y-2x-7y/xy^2

$$\frac { 5 x + 5 y } { 3 x ^ { 2 } y } - \frac { 2 x - 7 y } { x y ^ { 2 } }$$

Evaluate

$$\frac{5y^{2}+26xy-6x^{2}}{3\left(xy\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{2}y and xy^{2} is 3x^{2}y^{2}. Multiply \frac{5x+5y}{3x^{2}y} times \frac{y}{y}. Multiply \frac{2x-7y}{xy^{2}} times \frac{3x}{3x}.

$$\frac{\left(5x+5y\right)y}{3x^{2}y^{2}}-\frac{\left(2x-7y\right)\times 3x}{3x^{2}y^{2}}$$

Since \frac{\left(5x+5y\right)y}{3x^{2}y^{2}} and \frac{\left(2x-7y\right)\times 3x}{3x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x+5y\right)y-\left(2x-7y\right)\times 3x}{3x^{2}y^{2}}$$

Do the multiplications in \left(5x+5y\right)y-\left(2x-7y\right)\times 3x.

$$\frac{5xy+5y^{2}-6x^{2}+21yx}{3x^{2}y^{2}}$$

Combine like terms in 5xy+5y^{2}-6x^{2}+21yx.

$$\frac{5y^{2}+26xy-6x^{2}}{3x^{2}y^{2}}$$

Expand

$$\frac{5y^{2}+26xy-6x^{2}}{3\left(xy\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{2}y and xy^{2} is 3x^{2}y^{2}. Multiply \frac{5x+5y}{3x^{2}y} times \frac{y}{y}. Multiply \frac{2x-7y}{xy^{2}} times \frac{3x}{3x}.

$$\frac{\left(5x+5y\right)y}{3x^{2}y^{2}}-\frac{\left(2x-7y\right)\times 3x}{3x^{2}y^{2}}$$

Since \frac{\left(5x+5y\right)y}{3x^{2}y^{2}} and \frac{\left(2x-7y\right)\times 3x}{3x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x+5y\right)y-\left(2x-7y\right)\times 3x}{3x^{2}y^{2}}$$

Do the multiplications in \left(5x+5y\right)y-\left(2x-7y\right)\times 3x.

$$\frac{5xy+5y^{2}-6x^{2}+21yx}{3x^{2}y^{2}}$$

Combine like terms in 5xy+5y^{2}-6x^{2}+21yx.

$$\frac{5y^{2}+26xy-6x^{2}}{3x^{2}y^{2}}$$