Solve 7x/x-1-x^2+4/x

$$\frac { 7 x } { x - 1 } - \frac { x ^ { 2 } + 4 } { x }$$

Evaluate

$$\frac{4-4x+8x^{2}-x^{3}}{x\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x is x\left(x-1\right). Multiply \frac{7x}{x-1} times \frac{x}{x}. Multiply \frac{x^{2}+4}{x} times \frac{x-1}{x-1}.

$$\frac{7xx}{x\left(x-1\right)}-\frac{\left(x^{2}+4\right)\left(x-1\right)}{x\left(x-1\right)}$$

Since \frac{7xx}{x\left(x-1\right)} and \frac{\left(x^{2}+4\right)\left(x-1\right)}{x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7xx-\left(x^{2}+4\right)\left(x-1\right)}{x\left(x-1\right)}$$

Do the multiplications in 7xx-\left(x^{2}+4\right)\left(x-1\right).

$$\frac{7x^{2}-x^{3}+x^{2}-4x+4}{x\left(x-1\right)}$$

Combine like terms in 7x^{2}-x^{3}+x^{2}-4x+4.

$$\frac{8x^{2}-x^{3}-4x+4}{x\left(x-1\right)}$$

Expand x\left(x-1\right).

$$\frac{8x^{2}-x^{3}-4x+4}{x^{2}-x}$$

Expand

$$\frac{4-4x+8x^{2}-x^{3}}{x\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x is x\left(x-1\right). Multiply \frac{7x}{x-1} times \frac{x}{x}. Multiply \frac{x^{2}+4}{x} times \frac{x-1}{x-1}.

$$\frac{7xx}{x\left(x-1\right)}-\frac{\left(x^{2}+4\right)\left(x-1\right)}{x\left(x-1\right)}$$

Since \frac{7xx}{x\left(x-1\right)} and \frac{\left(x^{2}+4\right)\left(x-1\right)}{x\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7xx-\left(x^{2}+4\right)\left(x-1\right)}{x\left(x-1\right)}$$

Do the multiplications in 7xx-\left(x^{2}+4\right)\left(x-1\right).

$$\frac{7x^{2}-x^{3}+x^{2}-4x+4}{x\left(x-1\right)}$$

Combine like terms in 7x^{2}-x^{3}+x^{2}-4x+4.

$$\frac{8x^{2}-x^{3}-4x+4}{x\left(x-1\right)}$$

Expand x\left(x-1\right).

$$\frac{8x^{2}-x^{3}-4x+4}{x^{2}-x}$$