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

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

Evaluate

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

Short Solution Steps

Factor x^{2}-3x.

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

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

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

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

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

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

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

Combine like terms in 2x-3-3x^{2}-x.

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

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

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

Expand

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

Short Solution Steps

Factor x^{2}-3x.

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

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

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

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

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

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

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

Combine like terms in 2x-3-3x^{2}-x.

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

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

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