Solve 1/x-3-6/x^2-9-x-1/6+2x

$$\frac { 1 } { x - 3 } - \frac { 6 } { x ^ { 2 } - 9 } - \frac { x - 1 } { 6 + 2 x }$$

Evaluate

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

Short Solution Steps

Factor x^{2}-9.

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

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

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

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

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

Combine like terms in x+3-6.

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

Cancel out x-3 in both numerator and denominator.

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

Factor 6+2x.

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

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

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

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

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

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

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

Combine like terms in 2-x+1.

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

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

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

Expand

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

Short Solution Steps

Factor x^{2}-9.

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

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

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

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

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

Combine like terms in x+3-6.

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

Cancel out x-3 in both numerator and denominator.

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

Factor 6+2x.

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

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

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

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

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

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

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

Combine like terms in 2-x+1.

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

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

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