Solve frac{2x^{2}-3x+1}{x^{2}-4}div3x^2-x-2/x^2-x-6*3x^2-4x-4/2x^2-7x+3

$$\frac { 2 x ^ { 2 } - 3 x + 1 } { x ^ { 2 } - 4 } \div \frac { 3 x ^ { 2 } - x - 2 } { x ^ { 2 } - x - 6 } \cdot \frac { 3 x ^ { 2 } - 4 x - 4 } { 2 x ^ { 2 } - 7 x + 3 }$$

Evaluate

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Short Solution Steps

Divide \frac{2x^{2}-3x+1}{x^{2}-4} by \frac{3x^{2}-x-2}{x^{2}-x-6} by multiplying \frac{2x^{2}-3x+1}{x^{2}-4} by the reciprocal of \frac{3x^{2}-x-2}{x^{2}-x-6}.

$$\frac{\left(2x^{2}-3x+1\right)\left(x^{2}-x-6\right)}{\left(x^{2}-4\right)\left(3x^{2}-x-2\right)}\times \frac{3x^{2}-4x-4}{2x^{2}-7x+3}$$

Factor the expressions that are not already factored in \frac{\left(2x^{2}-3x+1\right)\left(x^{2}-x-6\right)}{\left(x^{2}-4\right)\left(3x^{2}-x-2\right)}.

$$\frac{\left(x-3\right)\left(x-1\right)\left(2x-1\right)\left(x+2\right)}{\left(x-2\right)\left(x-1\right)\left(x+2\right)\left(3x+2\right)}\times \frac{3x^{2}-4x-4}{2x^{2}-7x+3}$$

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

$$\frac{\left(x-3\right)\left(2x-1\right)}{\left(x-2\right)\left(3x+2\right)}\times \frac{3x^{2}-4x-4}{2x^{2}-7x+3}$$

Multiply \frac{\left(x-3\right)\left(2x-1\right)}{\left(x-2\right)\left(3x+2\right)} times \frac{3x^{2}-4x-4}{2x^{2}-7x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-3\right)\left(2x-1\right)\left(3x^{2}-4x-4\right)}{\left(x-2\right)\left(3x+2\right)\left(2x^{2}-7x+3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x-2\right)\left(2x-1\right)\left(3x+2\right) in both numerator and denominator.

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Factor

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