Solve 2x/3x^2-2/5x^2y

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

Evaluate

$$\frac{2}{3x}-\frac{2}{5yx^{2}}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 5x^{2}y is 15yx^{2}. Multiply \frac{2}{3x} times \frac{5xy}{5xy}. Multiply \frac{2}{5x^{2}y} times \frac{3}{3}.

$$\frac{2\times 5xy}{15yx^{2}}-\frac{2\times 3}{15yx^{2}}$$

Since \frac{2\times 5xy}{15yx^{2}} and \frac{2\times 3}{15yx^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 5xy-2\times 3}{15yx^{2}}$$

Do the multiplications in 2\times 5xy-2\times 3.

$$\frac{10xy-6}{15yx^{2}}$$

Factor

$$\frac{2\times \left(\frac{1}{x}\right)^{2}\left(5x-\frac{3}{y}\right)}{15}$$