Solve (1-5x-4/x+1)divx-2/x+1

$$(1- \frac{ 5x-4 }{ x+1 } ) \div \frac{ x-2 }{ x+1 }$$

Evaluate

$$\frac{5-4x}{x-2}$$

Short Solution Steps

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

$$\frac{\frac{x+1}{x+1}-\frac{5x-4}{x+1}}{\frac{x-2}{x+1}}$$

Since \frac{x+1}{x+1} and \frac{5x-4}{x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+1-\left(5x-4\right)}{x+1}}{\frac{x-2}{x+1}}$$

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

$$\frac{\frac{x+1-5x+4}{x+1}}{\frac{x-2}{x+1}}$$

Combine like terms in x+1-5x+4.

$$\frac{\frac{-4x+5}{x+1}}{\frac{x-2}{x+1}}$$

Divide \frac{-4x+5}{x+1} by \frac{x-2}{x+1} by multiplying \frac{-4x+5}{x+1} by the reciprocal of \frac{x-2}{x+1}.

$$\frac{\left(-4x+5\right)\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{-4x+5}{x-2}$$

Expand

$$\frac{5-4x}{x-2}$$

Short Solution Steps

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

$$\frac{\frac{x+1}{x+1}-\frac{5x-4}{x+1}}{\frac{x-2}{x+1}}$$

Since \frac{x+1}{x+1} and \frac{5x-4}{x+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+1-\left(5x-4\right)}{x+1}}{\frac{x-2}{x+1}}$$

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

$$\frac{\frac{x+1-5x+4}{x+1}}{\frac{x-2}{x+1}}$$

Combine like terms in x+1-5x+4.

$$\frac{\frac{-4x+5}{x+1}}{\frac{x-2}{x+1}}$$

Divide \frac{-4x+5}{x+1} by \frac{x-2}{x+1} by multiplying \frac{-4x+5}{x+1} by the reciprocal of \frac{x-2}{x+1}.

$$\frac{\left(-4x+5\right)\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{-4x+5}{x-2}$$