Solve (x-2)/(x+1)\div((x)^(2)-3x+2)/(x-2)\times(x+1)/(x-2)

Question

$$\frac{ x-2 }{ x+1 } \div \frac{ { x }^{ 2 } -3x+2 }{ x-2 } \times \frac{ x+1 }{ x-2 }$$

Evaluate

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

Short Solution Steps

Divide $\frac{x-2}{x+1}$ by $\frac{x^{2}-3x+2}{x-2}$ by multiplying $\frac{x-2}{x+1}$ by the reciprocal of $\frac{x^{2}-3x+2}{x-2}$.

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

Multiply $x-2$ and $x-2$ to get $\left(x-2\right)^{2}$.

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

Factor the expressions that are not already factored in $\frac{\left(x-2\right)^{2}}{\left(x+1\right)\left(x^{2}-3x+2\right)}$.

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

Cancel out $x-2$ in both numerator and denominator.

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

Multiply $\frac{x-2}{\left(x-1\right)\left(x+1\right)}$ times $\frac{x+1}{x-2}$ by multiplying numerator times numerator and denominator times denominator.

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

Cancel out $\left(x-2\right)\left(x+1\right)$ in both numerator and denominator.

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

Show Solution

Expand

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

Short Solution Steps

Divide $\frac{x-2}{x+1}$ by $\frac{x^{2}-3x+2}{x-2}$ by multiplying $\frac{x-2}{x+1}$ by the reciprocal of $\frac{x^{2}-3x+2}{x-2}$.

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

Multiply $x-2$ and $x-2$ to get $\left(x-2\right)^{2}$.

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

Factor the expressions that are not already factored in $\frac{\left(x-2\right)^{2}}{\left(x+1\right)\left(x^{2}-3x+2\right)}$.

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

Cancel out $x-2$ in both numerator and denominator.

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

Multiply $\frac{x-2}{\left(x-1\right)\left(x+1\right)}$ times $\frac{x+1}{x-2}$ by multiplying numerator times numerator and denominator times denominator.

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

Cancel out $\left(x-2\right)\left(x+1\right)$ in both numerator and denominator.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Evaluate

Short Solution Steps

Expand

Short Solution Steps