Solve 2*x-3/x^2-4*x+2/x^2-6x+9

$$2 \cdot \frac { x - 3 } { x ^ { 2 } - 4 } \cdot \frac { x + 2 } { x ^ { 2 } - 6 x + 9 }$$

Evaluate

$$\frac{2}{\left(x-3\right)\left(x-2\right)}$$

Short Solution Steps

Express 2\times \frac{x-3}{x^{2}-4} as a single fraction.

$$\frac{2\left(x-3\right)}{x^{2}-4}\times \frac{x+2}{x^{2}-6x+9}$$

Multiply \frac{2\left(x-3\right)}{x^{2}-4} times \frac{x+2}{x^{2}-6x+9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(x-3\right)\left(x+2\right)}{\left(x^{2}-4\right)\left(x^{2}-6x+9\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x+2\right) in both numerator and denominator.

$$\frac{2}{\left(x-3\right)\left(x-2\right)}$$

Expand the expression.

$$\frac{2}{x^{2}-5x+6}$$

Expand

$$\frac{2}{\left(x-3\right)\left(x-2\right)}$$

Short Solution Steps

Express 2\times \frac{x-3}{x^{2}-4} as a single fraction.

$$\frac{2\left(x-3\right)}{x^{2}-4}\times \frac{x+2}{x^{2}-6x+9}$$

Multiply \frac{2\left(x-3\right)}{x^{2}-4} times \frac{x+2}{x^{2}-6x+9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(x-3\right)\left(x+2\right)}{\left(x^{2}-4\right)\left(x^{2}-6x+9\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x+2\right) in both numerator and denominator.

$$\frac{2}{\left(x-3\right)\left(x-2\right)}$$

Expand the expression.

$$\frac{2}{x^{2}-5x+6}$$