Solve f(x)=2x-5/x(x-3)-12

$$f ( x ) = \frac { 2 x - 5 } { x ( x - 3 ) } - 12$$

Evaluate

$$\frac{-12x^{2}+38x-5}{x\left(x-3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 12 times \frac{x\left(x-3\right)}{x\left(x-3\right)}.

$$\frac{2x-5}{x\left(x-3\right)}-\frac{12x\left(x-3\right)}{x\left(x-3\right)}$$

Since \frac{2x-5}{x\left(x-3\right)} and \frac{12x\left(x-3\right)}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x-5-12x\left(x-3\right)}{x\left(x-3\right)}$$

Do the multiplications in 2x-5-12x\left(x-3\right).

$$\frac{2x-5-12x^{2}+36x}{x\left(x-3\right)}$$

Combine like terms in 2x-5-12x^{2}+36x.

$$\frac{38x-5-12x^{2}}{x\left(x-3\right)}$$

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

$$\frac{38x-5-12x^{2}}{x^{2}-3x}$$

Expand

$$\frac{-12x^{2}+38x-5}{x\left(x-3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 12 times \frac{x\left(x-3\right)}{x\left(x-3\right)}.

$$\frac{2x-5}{x\left(x-3\right)}-\frac{12x\left(x-3\right)}{x\left(x-3\right)}$$

Since \frac{2x-5}{x\left(x-3\right)} and \frac{12x\left(x-3\right)}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x-5-12x\left(x-3\right)}{x\left(x-3\right)}$$

Do the multiplications in 2x-5-12x\left(x-3\right).

$$\frac{2x-5-12x^{2}+36x}{x\left(x-3\right)}$$

Combine like terms in 2x-5-12x^{2}+36x.

$$\frac{38x-5-12x^{2}}{x\left(x-3\right)}$$

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

$$\frac{38x-5-12x^{2}}{x^{2}-3x}$$