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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in 5\times 2y+5x.

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

Factor the expressions that are not already factored in \frac{10y+5x}{10x^{2}y^{2}}.

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

Cancel out 5 in both numerator and denominator.

$$\frac{x+2y}{2x^{2}y^{2}}$$

Factor

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