Solve 2y-8/5xy^2+5-2x/10x^2y

$$\frac { 2 y - 8 } { 5 x y ^ { 2 } } + \frac { 5 - 2 x } { 10 x ^ { 2 } y }$$

Evaluate

$$\frac{2xy-16x+5y}{10\left(xy\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5xy^{2} and 10x^{2}y is 10x^{2}y^{2}. Multiply \frac{2y-8}{5xy^{2}} times \frac{2x}{2x}. Multiply \frac{5-2x}{10x^{2}y} times \frac{y}{y}.

$$\frac{\left(2y-8\right)\times 2x}{10x^{2}y^{2}}+\frac{\left(5-2x\right)y}{10x^{2}y^{2}}$$

Since \frac{\left(2y-8\right)\times 2x}{10x^{2}y^{2}} and \frac{\left(5-2x\right)y}{10x^{2}y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2y-8\right)\times 2x+\left(5-2x\right)y}{10x^{2}y^{2}}$$

Do the multiplications in \left(2y-8\right)\times 2x+\left(5-2x\right)y.

$$\frac{4yx-16x+5y-2xy}{10x^{2}y^{2}}$$

Combine like terms in 4yx-16x+5y-2xy.

$$\frac{2yx-16x+5y}{10x^{2}y^{2}}$$

Expand

$$\frac{2xy-16x+5y}{10\left(xy\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5xy^{2} and 10x^{2}y is 10x^{2}y^{2}. Multiply \frac{2y-8}{5xy^{2}} times \frac{2x}{2x}. Multiply \frac{5-2x}{10x^{2}y} times \frac{y}{y}.

$$\frac{\left(2y-8\right)\times 2x}{10x^{2}y^{2}}+\frac{\left(5-2x\right)y}{10x^{2}y^{2}}$$

Since \frac{\left(2y-8\right)\times 2x}{10x^{2}y^{2}} and \frac{\left(5-2x\right)y}{10x^{2}y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2y-8\right)\times 2x+\left(5-2x\right)y}{10x^{2}y^{2}}$$

Do the multiplications in \left(2y-8\right)\times 2x+\left(5-2x\right)y.

$$\frac{4yx-16x+5y-2xy}{10x^{2}y^{2}}$$

Combine like terms in 4yx-16x+5y-2xy.

$$\frac{2yx-16x+5y}{10x^{2}y^{2}}$$