Solve [(x-1)^2/x(x-1)-(4+x)(4-x)/x(x+2)]

$$[ \frac { ( x - 1 ) ^ { 2 } } { x ( x - 1 ) } - \frac { ( 4 + x ) ( 4 - x ) } { x ( x + 2 ) } ]$$

Evaluate

$$\frac{2x^{2}+x-18}{x\left(x+2\right)}$$

Short Solution Steps

Cancel out x-1 in both numerator and denominator.

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

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

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

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

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

Do the multiplications in \left(x-1\right)\left(x+2\right)-\left(4+x\right)\left(4-x\right).

$$\frac{x^{2}+2x-x-2-16+4x-4x+x^{2}}{x\left(x+2\right)}$$

Combine like terms in x^{2}+2x-x-2-16+4x-4x+x^{2}.

$$\frac{2x^{2}+x-18}{x\left(x+2\right)}$$

Expand x\left(x+2\right).

$$\frac{2x^{2}+x-18}{x^{2}+2x}$$

Expand

$$\frac{2x^{2}+x-18}{x\left(x+2\right)}$$

Short Solution Steps

Cancel out x-1 in both numerator and denominator.

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

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

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

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

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

Do the multiplications in \left(x-1\right)\left(x+2\right)-\left(4+x\right)\left(4-x\right).

$$\frac{x^{2}+2x-x-2-16+4x-4x+x^{2}}{x\left(x+2\right)}$$

Combine like terms in x^{2}+2x-x-2-16+4x-4x+x^{2}.

$$\frac{2x^{2}+x-18}{x\left(x+2\right)}$$

Expand x\left(x+2\right).

$$\frac{2x^{2}+x-18}{x^{2}+2x}$$