Solve 5x-2y/10x^2-6y/20xy

$$\frac { 5 x - 2 y } { 10 x ^ { 2 } } - \frac { 6 y } { 20 x y }$$

Evaluate

$$\frac{x-y}{5x^{2}}$$

Short Solution Steps

Cancel out 2y in both numerator and denominator.

$$\frac{5x-2y}{10x^{2}}-\frac{3}{10x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10x^{2} and 10x is 10x^{2}. Multiply \frac{3}{10x} times \frac{x}{x}.

$$\frac{5x-2y}{10x^{2}}-\frac{3x}{10x^{2}}$$

Since \frac{5x-2y}{10x^{2}} and \frac{3x}{10x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-2y-3x}{10x^{2}}$$

Combine like terms in 5x-2y-3x.

$$\frac{2x-2y}{10x^{2}}$$

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

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

Cancel out 2 in both numerator and denominator.

$$\frac{x-y}{5x^{2}}$$

Expand

$$-\frac{y-x}{5x^{2}}$$

Short Solution Steps

Cancel out 2y in both numerator and denominator.

$$\frac{5x-2y}{10x^{2}}-\frac{3}{10x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10x^{2} and 10x is 10x^{2}. Multiply \frac{3}{10x} times \frac{x}{x}.

$$\frac{5x-2y}{10x^{2}}-\frac{3x}{10x^{2}}$$

Since \frac{5x-2y}{10x^{2}} and \frac{3x}{10x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-2y-3x}{10x^{2}}$$

Combine like terms in 5x-2y-3x.

$$\frac{2x-2y}{10x^{2}}$$

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

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

Cancel out 2 in both numerator and denominator.

$$\frac{x-y}{5x^{2}}$$