Solve (x+4x+3/x+1-4):(x-1)

$$( \frac { x + 4 x + 3 } { x + 1 } - 4 ) : ( x - 1 )$$

Evaluate

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

Short Solution Steps

Combine x and 4x to get 5x.

$$\frac{\frac{5x+3}{x+1}-4}{x-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x+1}{x+1}.

$$\frac{\frac{5x+3}{x+1}-\frac{4\left(x+1\right)}{x+1}}{x-1}$$

Since \frac{5x+3}{x+1} and \frac{4\left(x+1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x+3-4\left(x+1\right)}{x+1}}{x-1}$$

Do the multiplications in 5x+3-4\left(x+1\right).

$$\frac{\frac{5x+3-4x-4}{x+1}}{x-1}$$

Combine like terms in 5x+3-4x-4.

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Combine x and 4x to get 5x.

$$\frac{\frac{5x+3}{x+1}-4}{x-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x+1}{x+1}.

$$\frac{\frac{5x+3}{x+1}-\frac{4\left(x+1\right)}{x+1}}{x-1}$$

Since \frac{5x+3}{x+1} and \frac{4\left(x+1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x+3-4\left(x+1\right)}{x+1}}{x-1}$$

Do the multiplications in 5x+3-4\left(x+1\right).

$$\frac{\frac{5x+3-4x-4}{x+1}}{x-1}$$

Combine like terms in 5x+3-4x-4.

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

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

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

Cancel out x-1 in both numerator and denominator.

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