Solve (x-1)^2/4x^2-1*2x^2-3x-2/x^2-4x+3

$$\frac { ( x - 1 ) ^ { 2 } } { 4 x ^ { 2 } - 1 } \times \frac { 2 x ^ { 2 } - 3 x - 2 } { x ^ { 2 } - 4 x + 3 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{\left(x-1\right)^{2}}{4x^{2}-1} times \frac{2x^{2}-3x-2}{x^{2}-4x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-1\right)^{2}\left(2x^{2}-3x-2\right)}{\left(4x^{2}-1\right)\left(x^{2}-4x+3\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{x^{2}-3x+2}{2x^{2}-7x+3}$$

Expand

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

Short Solution Steps

Multiply \frac{\left(x-1\right)^{2}}{4x^{2}-1} times \frac{2x^{2}-3x-2}{x^{2}-4x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-1\right)^{2}\left(2x^{2}-3x-2\right)}{\left(4x^{2}-1\right)\left(x^{2}-4x+3\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{x^{2}-3x+2}{2x^{2}-7x+3}$$