Solve =x/4-x-2(x-12)/x(x-4)

$$= \frac { x } { 4 - x } - \frac { 2 ( x - 12 ) } { x ( x - 4 ) }$$

Evaluate

$$-1-\frac{6}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4-x and x\left(x-4\right) is x\left(x-4\right). Multiply \frac{x}{4-x} times \frac{-x}{-x}.

$$\frac{x\left(-1\right)x}{x\left(x-4\right)}-\frac{2\left(x-12\right)}{x\left(x-4\right)}$$

Since \frac{x\left(-1\right)x}{x\left(x-4\right)} and \frac{2\left(x-12\right)}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(-1\right)x-2\left(x-12\right)}{x\left(x-4\right)}$$

Do the multiplications in x\left(-1\right)x-2\left(x-12\right).

$$\frac{-x^{2}-2x+24}{x\left(x-4\right)}$$

Factor the expressions that are not already factored in \frac{-x^{2}-2x+24}{x\left(x-4\right)}.

$$\frac{\left(x+6\right)\left(-x+4\right)}{x\left(x-4\right)}$$

Extract the negative sign in 4-x.

$$\frac{-\left(x-4\right)\left(x+6\right)}{x\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

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

To find the opposite of x+6, find the opposite of each term.

$$\frac{-x-6}{x}$$

Expand

$$-1-\frac{6}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4-x and x\left(x-4\right) is x\left(x-4\right). Multiply \frac{x}{4-x} times \frac{-x}{-x}.

$$\frac{x\left(-1\right)x}{x\left(x-4\right)}-\frac{2\left(x-12\right)}{x\left(x-4\right)}$$

Since \frac{x\left(-1\right)x}{x\left(x-4\right)} and \frac{2\left(x-12\right)}{x\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\left(-1\right)x-2\left(x-12\right)}{x\left(x-4\right)}$$

Do the multiplications in x\left(-1\right)x-2\left(x-12\right).

$$\frac{-x^{2}-2x+24}{x\left(x-4\right)}$$

Factor the expressions that are not already factored in \frac{-x^{2}-2x+24}{x\left(x-4\right)}.

$$\frac{\left(x+6\right)\left(-x+4\right)}{x\left(x-4\right)}$$

Extract the negative sign in 4-x.

$$\frac{-\left(x-4\right)\left(x+6\right)}{x\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

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

To find the opposite of x+6, find the opposite of each term.

$$\frac{-x-6}{x}$$