Solve 2x/5y+4y/3x-x/y+3x/2y

$$\frac{ 2x }{ 5y } + \frac{ 4y }{ 3x } - \frac{ x }{ y } + \frac{ 3x }{ 2y }$$

Evaluate

$$\frac{27x^{2}+40y^{2}}{30xy}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5y and 3x is 15xy. Multiply \frac{2x}{5y} times \frac{3x}{3x}. Multiply \frac{4y}{3x} times \frac{5y}{5y}.

$$\frac{2x\times 3x}{15xy}+\frac{4y\times 5y}{15xy}-\frac{x}{y}+\frac{3x}{2y}$$

Since \frac{2x\times 3x}{15xy} and \frac{4y\times 5y}{15xy} have the same denominator, add them by adding their numerators.

$$\frac{2x\times 3x+4y\times 5y}{15xy}-\frac{x}{y}+\frac{3x}{2y}$$

Do the multiplications in 2x\times 3x+4y\times 5y.

$$\frac{6x^{2}+20y^{2}}{15xy}-\frac{x}{y}+\frac{3x}{2y}$$

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

$$\frac{6x^{2}+20y^{2}}{15xy}-\frac{x\times 15x}{15xy}+\frac{3x}{2y}$$

Since \frac{6x^{2}+20y^{2}}{15xy} and \frac{x\times 15x}{15xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x^{2}+20y^{2}-x\times 15x}{15xy}+\frac{3x}{2y}$$

Do the multiplications in 6x^{2}+20y^{2}-x\times 15x.

$$\frac{6x^{2}+20y^{2}-15x^{2}}{15xy}+\frac{3x}{2y}$$

Combine like terms in 6x^{2}+20y^{2}-15x^{2}.

$$\frac{-9x^{2}+20y^{2}}{15xy}+\frac{3x}{2y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15xy and 2y is 30xy. Multiply \frac{-9x^{2}+20y^{2}}{15xy} times \frac{2}{2}. Multiply \frac{3x}{2y} times \frac{15x}{15x}.

$$\frac{2\left(-9x^{2}+20y^{2}\right)}{30xy}+\frac{3x\times 15x}{30xy}$$

Since \frac{2\left(-9x^{2}+20y^{2}\right)}{30xy} and \frac{3x\times 15x}{30xy} have the same denominator, add them by adding their numerators.

$$\frac{2\left(-9x^{2}+20y^{2}\right)+3x\times 15x}{30xy}$$

Do the multiplications in 2\left(-9x^{2}+20y^{2}\right)+3x\times 15x.

$$\frac{-18x^{2}+40y^{2}+45x^{2}}{30xy}$$

Combine like terms in -18x^{2}+40y^{2}+45x^{2}.

$$\frac{27x^{2}+40y^{2}}{30xy}$$

Factor

$$\frac{27x^{2}+40y^{2}}{30xy}$$