Solve left(5x/2+2x/3right)left(5x/2-2x/3right)

$$\left( \frac{ 5x }{ 2 } + \frac{ 2x }{ 3 } \right) \left( \frac{ 5x }{ 2 } - \frac{ 2x }{ 3 } \right)$$

Evaluate

$$\frac{209x^{2}}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5x}{2} times \frac{3}{3}. Multiply \frac{2x}{3} times \frac{2}{2}.

$$\left(\frac{3\times 5x}{6}+\frac{2\times 2x}{6}\right)\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

Since \frac{3\times 5x}{6} and \frac{2\times 2x}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\times 5x+2\times 2x}{6}\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

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

$$\frac{15x+4x}{6}\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

Combine like terms in 15x+4x.

$$\frac{19x}{6}\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5x}{2} times \frac{3}{3}. Multiply \frac{2x}{3} times \frac{2}{2}.

$$\frac{19x}{6}\left(\frac{3\times 5x}{6}-\frac{2\times 2x}{6}\right)$$

Since \frac{3\times 5x}{6} and \frac{2\times 2x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19x}{6}\times \frac{3\times 5x-2\times 2x}{6}$$

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

$$\frac{19x}{6}\times \frac{15x-4x}{6}$$

Combine like terms in 15x-4x.

$$\frac{19x}{6}\times \frac{11x}{6}$$

Multiply \frac{19x}{6} times \frac{11x}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19x\times 11x}{6\times 6}$$

Multiply x and x to get x^{2}.

$$\frac{19x^{2}\times 11}{6\times 6}$$

Multiply 19 and 11 to get 209.

$$\frac{209x^{2}}{6\times 6}$$

Multiply 6 and 6 to get 36.

$$\frac{209x^{2}}{36}$$

Expand

$$\frac{209x^{2}}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5x}{2} times \frac{3}{3}. Multiply \frac{2x}{3} times \frac{2}{2}.

$$\left(\frac{3\times 5x}{6}+\frac{2\times 2x}{6}\right)\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

Since \frac{3\times 5x}{6} and \frac{2\times 2x}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\times 5x+2\times 2x}{6}\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

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

$$\frac{15x+4x}{6}\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

Combine like terms in 15x+4x.

$$\frac{19x}{6}\left(\frac{5x}{2}-\frac{2x}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5x}{2} times \frac{3}{3}. Multiply \frac{2x}{3} times \frac{2}{2}.

$$\frac{19x}{6}\left(\frac{3\times 5x}{6}-\frac{2\times 2x}{6}\right)$$

Since \frac{3\times 5x}{6} and \frac{2\times 2x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19x}{6}\times \frac{3\times 5x-2\times 2x}{6}$$

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

$$\frac{19x}{6}\times \frac{15x-4x}{6}$$

Combine like terms in 15x-4x.

$$\frac{19x}{6}\times \frac{11x}{6}$$

Multiply \frac{19x}{6} times \frac{11x}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19x\times 11x}{6\times 6}$$

Multiply x and x to get x^{2}.

$$\frac{19x^{2}\times 11}{6\times 6}$$

Multiply 19 and 11 to get 209.

$$\frac{209x^{2}}{6\times 6}$$

Multiply 6 and 6 to get 36.

$$\frac{209x^{2}}{36}$$