Solve 4x^2-10x+6/x^4-3x^3div2x-3/2x^3*x-3/2x-2=

$$\frac { 4 x ^ { 2 } - 10 x + 6 } { x ^ { 4 } - 3 x ^ { 3 } } \div \frac { 2 x - 3 } { 2 x ^ { 3 } } \times \frac { x - 3 } { 2 x - 2 } =$$

Evaluate

$$2$$

Short Solution Steps

Divide \frac{4x^{2}-10x+6}{x^{4}-3x^{3}} by \frac{2x-3}{2x^{3}} by multiplying \frac{4x^{2}-10x+6}{x^{4}-3x^{3}} by the reciprocal of \frac{2x-3}{2x^{3}}.

$$\frac{\left(4x^{2}-10x+6\right)\times 2x^{3}}{\left(x^{4}-3x^{3}\right)\left(2x-3\right)}\times \frac{x-3}{2x-2}$$

Factor the expressions that are not already factored in \frac{\left(4x^{2}-10x+6\right)\times 2x^{3}}{\left(x^{4}-3x^{3}\right)\left(2x-3\right)}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Cancel out x-3 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

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

$$2$$

Factor

$$2$$