Solve x^2/3-3y^2/frac{3{2}(x-3y)}=

$$\frac { \frac { x ^ { 2 } } { 3 } - 3 y ^ { 2 } } { \frac { 3 } { 2 } ( x - 3 y ) } =$$

Evaluate

$$\frac{2\left(x+3y\right)}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -3y^{2} times \frac{3}{3}.

$$\frac{\frac{x^{2}}{3}+\frac{3\left(-3\right)y^{2}}{3}}{\frac{3}{2}\left(x-3y\right)}$$

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

$$\frac{\frac{x^{2}+3\left(-3\right)y^{2}}{3}}{\frac{3}{2}\left(x-3y\right)}$$

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

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

Express \frac{\frac{x^{2}-9y^{2}}{3}}{\frac{3}{2}\left(x-3y\right)} as a single fraction.

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

Multiply 3 and \frac{3}{2} to get \frac{9}{2}.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-3y\right)\left(x+3y\right)}{\frac{9}{2}\left(x-3y\right)}$$

Cancel out x-3y in both numerator and denominator.

$$\frac{x+3y}{\frac{9}{2}}$$

Divide x+3y by \frac{9}{2} by multiplying x+3y by the reciprocal of \frac{9}{2}.

$$\frac{\left(x+3y\right)\times 2}{9}$$

Use the distributive property to multiply x+3y by 2.

$$\frac{2x+6y}{9}$$

Expand

$$\frac{2x}{9}+\frac{2y}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -3y^{2} times \frac{3}{3}.

$$\frac{\frac{x^{2}}{3}+\frac{3\left(-3\right)y^{2}}{3}}{\frac{3}{2}\left(x-3y\right)}$$

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

$$\frac{\frac{x^{2}+3\left(-3\right)y^{2}}{3}}{\frac{3}{2}\left(x-3y\right)}$$

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

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

Express \frac{\frac{x^{2}-9y^{2}}{3}}{\frac{3}{2}\left(x-3y\right)} as a single fraction.

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

Multiply 3 and \frac{3}{2} to get \frac{9}{2}.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-3y\right)\left(x+3y\right)}{\frac{9}{2}\left(x-3y\right)}$$

Cancel out x-3y in both numerator and denominator.

$$\frac{x+3y}{\frac{9}{2}}$$

Divide x+3y by \frac{9}{2} by multiplying x+3y by the reciprocal of \frac{9}{2}.

$$\frac{\left(x+3y\right)\times 2}{9}$$

Use the distributive property to multiply x+3y by 2.

$$\frac{2x+6y}{9}$$