Solve x/70-x-12(710-x)+0

$$\frac { x } { 70 - x } - 12 ( 710 - x ) + 0$$

Evaluate

$$\frac{-12x^{2}+9361x-596400}{70-x}$$

Short Solution Steps

Anything plus zero gives itself.

$$\frac{x}{70-x}-12\left(710-x\right)$$

Use the distributive property to multiply -12 by 710-x.

$$\frac{x}{70-x}-8520+12x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -8520+12x times \frac{70-x}{70-x}.

$$\frac{x}{70-x}+\frac{\left(-8520+12x\right)\left(70-x\right)}{70-x}$$

Since \frac{x}{70-x} and \frac{\left(-8520+12x\right)\left(70-x\right)}{70-x} have the same denominator, add them by adding their numerators.

$$\frac{x+\left(-8520+12x\right)\left(70-x\right)}{70-x}$$

Do the multiplications in x+\left(-8520+12x\right)\left(70-x\right).

$$\frac{x-596400+8520x+840x-12x^{2}}{70-x}$$

Combine like terms in x-596400+8520x+840x-12x^{2}.

$$\frac{9361x-596400-12x^{2}}{70-x}$$

Expand

$$\frac{-12x^{2}+9361x-596400}{70-x}$$

Short Solution Steps

Anything plus zero gives itself.

$$\frac{x}{70-x}-12\left(710-x\right)$$

Use the distributive property to multiply -12 by 710-x.

$$\frac{x}{70-x}-8520+12x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -8520+12x times \frac{70-x}{70-x}.

$$\frac{x}{70-x}+\frac{\left(-8520+12x\right)\left(70-x\right)}{70-x}$$

Since \frac{x}{70-x} and \frac{\left(-8520+12x\right)\left(70-x\right)}{70-x} have the same denominator, add them by adding their numerators.

$$\frac{x+\left(-8520+12x\right)\left(70-x\right)}{70-x}$$

Do the multiplications in x+\left(-8520+12x\right)\left(70-x\right).

$$\frac{x-596400+8520x+840x-12x^{2}}{70-x}$$

Combine like terms in x-596400+8520x+840x-12x^{2}.

$$\frac{9361x-596400-12x^{2}}{70-x}$$