Solve 2/x+3-6x/2x+1

$$\frac { 2 } { x + 3 } - \frac { 6 x } { 2 x + 1 }$$

Evaluate

$$\frac{2\left(1-7x-3x^{2}\right)}{\left(x+3\right)\left(2x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and 2x+1 is \left(x+3\right)\left(2x+1\right). Multiply \frac{2}{x+3} times \frac{2x+1}{2x+1}. Multiply \frac{6x}{2x+1} times \frac{x+3}{x+3}.

$$\frac{2\left(2x+1\right)}{\left(x+3\right)\left(2x+1\right)}-\frac{6x\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)}$$

Since \frac{2\left(2x+1\right)}{\left(x+3\right)\left(2x+1\right)} and \frac{6x\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(2x+1\right)-6x\left(x+3\right)}{\left(x+3\right)\left(2x+1\right)}$$

Do the multiplications in 2\left(2x+1\right)-6x\left(x+3\right).

$$\frac{4x+2-6x^{2}-18x}{\left(x+3\right)\left(2x+1\right)}$$

Combine like terms in 4x+2-6x^{2}-18x.

$$\frac{-14x+2-6x^{2}}{\left(x+3\right)\left(2x+1\right)}$$

Expand \left(x+3\right)\left(2x+1\right).

$$\frac{-14x+2-6x^{2}}{2x^{2}+7x+3}$$

Factor

$$-\frac{6\left(x-\frac{-\sqrt{61}-7}{6}\right)\left(x-\frac{\sqrt{61}-7}{6}\right)}{\left(x+3\right)\left(2x+1\right)}$$