Solve 8024x-12028/(x-1)-(4013-x)

$$\frac{ 8024x-12028 }{ (x-1) } -(4013-x)$$

Evaluate

$$\frac{x^{2}+4010x-8015}{x-1}$$

Short Solution Steps

To find the opposite of 4013-x, find the opposite of each term.

$$\frac{8024x-12028}{x-1}-4013-\left(-x\right)$$

The opposite of -x is x.

$$\frac{8024x-12028}{x-1}-4013+x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4013+x times \frac{x-1}{x-1}.

$$\frac{8024x-12028}{x-1}+\frac{\left(-4013+x\right)\left(x-1\right)}{x-1}$$

Since \frac{8024x-12028}{x-1} and \frac{\left(-4013+x\right)\left(x-1\right)}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{8024x-12028+\left(-4013+x\right)\left(x-1\right)}{x-1}$$

Do the multiplications in 8024x-12028+\left(-4013+x\right)\left(x-1\right).

$$\frac{8024x-12028-4013x+4013+x^{2}-x}{x-1}$$

Combine like terms in 8024x-12028-4013x+4013+x^{2}-x.

$$\frac{4010x-8015+x^{2}}{x-1}$$

Expand

$$\frac{x^{2}+4010x-8015}{x-1}$$

Short Solution Steps

To find the opposite of 4013-x, find the opposite of each term.

$$\frac{8024x-12028}{x-1}-4013-\left(-x\right)$$

The opposite of -x is x.

$$\frac{8024x-12028}{x-1}-4013+x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4013+x times \frac{x-1}{x-1}.

$$\frac{8024x-12028}{x-1}+\frac{\left(-4013+x\right)\left(x-1\right)}{x-1}$$

Since \frac{8024x-12028}{x-1} and \frac{\left(-4013+x\right)\left(x-1\right)}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{8024x-12028+\left(-4013+x\right)\left(x-1\right)}{x-1}$$

Do the multiplications in 8024x-12028+\left(-4013+x\right)\left(x-1\right).

$$\frac{8024x-12028-4013x+4013+x^{2}-x}{x-1}$$

Combine like terms in 8024x-12028-4013x+4013+x^{2}-x.

$$\frac{4010x-8015+x^{2}}{x-1}$$