Solve 5/1+x-5/x

$$\frac{ \frac{ 5 }{ 1+x } -5 }{ x }$$

Evaluate

$$-\frac{5}{x+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{1+x}{1+x}.

$$\frac{\frac{5}{1+x}-\frac{5\left(1+x\right)}{1+x}}{x}$$

Since \frac{5}{1+x} and \frac{5\left(1+x\right)}{1+x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-5\left(1+x\right)}{1+x}}{x}$$

Do the multiplications in 5-5\left(1+x\right).

$$\frac{\frac{5-5-5x}{1+x}}{x}$$

Combine like terms in 5-5-5x.

$$\frac{\frac{-5x}{1+x}}{x}$$

Express \frac{\frac{-5x}{1+x}}{x} as a single fraction.

$$\frac{-5x}{\left(1+x\right)x}$$

Cancel out x in both numerator and denominator.

$$\frac{-5}{x+1}$$

Expand

$$-\frac{5}{x+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{1+x}{1+x}.

$$\frac{\frac{5}{1+x}-\frac{5\left(1+x\right)}{1+x}}{x}$$

Since \frac{5}{1+x} and \frac{5\left(1+x\right)}{1+x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-5\left(1+x\right)}{1+x}}{x}$$

Do the multiplications in 5-5\left(1+x\right).

$$\frac{\frac{5-5-5x}{1+x}}{x}$$

Combine like terms in 5-5-5x.

$$\frac{\frac{-5x}{1+x}}{x}$$

Express \frac{\frac{-5x}{1+x}}{x} as a single fraction.

$$\frac{-5x}{\left(1+x\right)x}$$

Cancel out x in both numerator and denominator.

$$\frac{-5}{x+1}$$