Solve 18x^2y/4x*3y^2/5x^2-36x^2/10x

$$\frac { 18 x ^ { 2 } y } { 4 x } \times \frac { 3 y ^ { 2 } } { 5 x ^ { 2 } } - \frac { 36 x ^ { 2 } } { 10 x }$$

Evaluate

$$\frac{27y^{3}}{10x}-\frac{18x}{5}$$

Short Solution Steps

Cancel out 2x in both numerator and denominator.

$$\frac{9xy}{2}\times \frac{3y^{2}}{5x^{2}}-\frac{36x^{2}}{10x}$$

Multiply \frac{9xy}{2} times \frac{3y^{2}}{5x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9xy\times 3y^{2}}{2\times 5x^{2}}-\frac{36x^{2}}{10x}$$

Cancel out x in both numerator and denominator.

$$\frac{3\times 9yy^{2}}{2\times 5x}-\frac{36x^{2}}{10x}$$

Cancel out 2x in both numerator and denominator.

$$\frac{3\times 9yy^{2}}{2\times 5x}-\frac{18x}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\times 5x and 5 is 2\times 5x. Multiply \frac{18x}{5} times \frac{2x}{2x}.

$$\frac{3\times 9yy^{2}}{2\times 5x}-\frac{18x\times 2x}{2\times 5x}$$

Since \frac{3\times 9yy^{2}}{2\times 5x} and \frac{18x\times 2x}{2\times 5x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 9yy^{2}-18x\times 2x}{2\times 5x}$$

Do the multiplications in 3\times 9yy^{2}-18x\times 2x.

$$\frac{27y^{3}-36x^{2}}{2\times 5x}$$

Expand 2\times 5x.

$$\frac{27y^{3}-36x^{2}}{10x}$$

Factor

$$\frac{9\left(3y^{3}-4x^{2}\right)}{10x}$$