Solve s-1/x^3-3x^2-x+3div5x-2/x^2-6x+9

$$\frac { s - 1 } { x ^ { 3 } - 3 x ^ { 2 } - x + 3 } \div \frac { 5 x - 2 } { x ^ { 2 } - 6 x + 9 }$$

Evaluate

$$\frac{\left(s-1\right)\left(x-3\right)}{\left(5x-2\right)\left(x^{2}-1\right)}$$

$$x\neq 3\text{ and }x\neq \frac{2}{5}\text{ and }|x|\neq 1$$

Short Solution Steps

Divide \frac{s-1}{x^{3}-3x^{2}-x+3} by \frac{5x-2}{x^{2}-6x+9} by multiplying \frac{s-1}{x^{3}-3x^{2}-x+3} by the reciprocal of \frac{5x-2}{x^{2}-6x+9}.

$$\frac{\left(s-1\right)\left(x^{2}-6x+9\right)}{\left(x^{3}-3x^{2}-x+3\right)\left(5x-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(s-1\right)\left(x-3\right)^{2}}{\left(x-3\right)\left(x-1\right)\left(5x-2\right)\left(x+1\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{\left(s-1\right)\left(x-3\right)}{\left(x-1\right)\left(5x-2\right)\left(x+1\right)}$$

Expand the expression.

$$\frac{sx-x-3s+3}{5x^{3}-2x^{2}-5x+2}$$

Expand

$$\frac{sx-x-3s+3}{\left(5x-2\right)\left(x^{2}-1\right)}$$

$$x\neq 3\text{ and }x\neq \frac{2}{5}\text{ and }|x|\neq 1$$

Short Solution Steps

Divide \frac{s-1}{x^{3}-3x^{2}-x+3} by \frac{5x-2}{x^{2}-6x+9} by multiplying \frac{s-1}{x^{3}-3x^{2}-x+3} by the reciprocal of \frac{5x-2}{x^{2}-6x+9}.

$$\frac{\left(s-1\right)\left(x^{2}-6x+9\right)}{\left(x^{3}-3x^{2}-x+3\right)\left(5x-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(s-1\right)\left(x-3\right)^{2}}{\left(x-3\right)\left(x-1\right)\left(5x-2\right)\left(x+1\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{\left(s-1\right)\left(x-3\right)}{\left(x-1\right)\left(5x-2\right)\left(x+1\right)}$$

Expand the expression.

$$\frac{sx-x-3s+3}{5x^{3}-2x^{2}-5x+2}$$