Solve 2x+2/3x-3x/x+3

$$\frac { 2 x + 2 } { 3 x } - \frac { 3 x } { x + 3 }$$

Evaluate

$$\frac{6+8x-7x^{2}}{3x\left(x+3\right)}$$

Short Solution Steps

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

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

Since \frac{\left(2x+2\right)\left(x+3\right)}{3x\left(x+3\right)} and \frac{3x\times 3x}{3x\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(2x+2\right)\left(x+3\right)-3x\times 3x.

$$\frac{2x^{2}+6x+2x+6-9x^{2}}{3x\left(x+3\right)}$$

Combine like terms in 2x^{2}+6x+2x+6-9x^{2}.

$$\frac{-7x^{2}+8x+6}{3x\left(x+3\right)}$$

Expand 3x\left(x+3\right).

$$\frac{-7x^{2}+8x+6}{3x^{2}+9x}$$

Expand

$$-\frac{7x^{2}-8x-6}{3x\left(x+3\right)}$$

Short Solution Steps

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

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

Since \frac{\left(2x+2\right)\left(x+3\right)}{3x\left(x+3\right)} and \frac{3x\times 3x}{3x\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(2x+2\right)\left(x+3\right)-3x\times 3x.

$$\frac{2x^{2}+6x+2x+6-9x^{2}}{3x\left(x+3\right)}$$

Combine like terms in 2x^{2}+6x+2x+6-9x^{2}.

$$\frac{-7x^{2}+8x+6}{3x\left(x+3\right)}$$

Expand 3x\left(x+3\right).

$$\frac{-7x^{2}+8x+6}{3x^{2}+9x}$$