Solve 4x^2+3x-3/x^2-3x/frac{1(x-2){x}}

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

Evaluate

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

Short Solution Steps

Divide \frac{4x^{2}+3x-3}{x^{2}-3x} by \frac{1\left(x-2\right)}{x} by multiplying \frac{4x^{2}+3x-3}{x^{2}-3x} by the reciprocal of \frac{1\left(x-2\right)}{x}.

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

Factor the expressions that are not already factored.

$$\frac{4x\left(x-\left(-\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)}{x\left(x-3\right)\left(x-2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{4\left(x-\left(-\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)}{\left(x-3\right)\left(x-2\right)}$$

Expand the expression.

$$\frac{4x^{2}+3x-3}{x^{2}-5x+6}$$

Expand

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

Short Solution Steps

Divide \frac{4x^{2}+3x-3}{x^{2}-3x} by \frac{1\left(x-2\right)}{x} by multiplying \frac{4x^{2}+3x-3}{x^{2}-3x} by the reciprocal of \frac{1\left(x-2\right)}{x}.

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

Factor the expressions that are not already factored.

$$\frac{4x\left(x-\left(-\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)}{x\left(x-3\right)\left(x-2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{4\left(x-\left(-\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)\left(x-\left(\frac{1}{8}\sqrt{57}-\frac{3}{8}\right)\right)}{\left(x-3\right)\left(x-2\right)}$$

Expand the expression.

$$\frac{4x^{2}+3x-3}{x^{2}-5x+6}$$