Solve x^2-5x+6/6xy^3/frac{x^2+3x-10{10x^3{y}^3}}

$$\frac{ \frac{ { x }^{ 2 } -5x+6 }{ 6x { y }^{ 3 } } }{ \frac{ { x }^{ 2 } +3x-10 }{ 10 { x }^{ 3 } { y }^{ 3 } } }$$

Evaluate

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

Short Solution Steps

Divide \frac{x^{2}-5x+6}{6xy^{3}} by \frac{x^{2}+3x-10}{10x^{3}y^{3}} by multiplying \frac{x^{2}-5x+6}{6xy^{3}} by the reciprocal of \frac{x^{2}+3x-10}{10x^{3}y^{3}}.

$$\frac{\left(x^{2}-5x+6\right)\times 10x^{3}y^{3}}{6xy^{3}\left(x^{2}+3x-10\right)}$$

Cancel out 2xy^{3} in both numerator and denominator.

$$\frac{5x^{2}\left(x^{2}-5x+6\right)}{3\left(x^{2}+3x-10\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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

Expand the expression.

$$\frac{5x^{3}-15x^{2}}{3x+15}$$

Expand

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

Short Solution Steps

Divide \frac{x^{2}-5x+6}{6xy^{3}} by \frac{x^{2}+3x-10}{10x^{3}y^{3}} by multiplying \frac{x^{2}-5x+6}{6xy^{3}} by the reciprocal of \frac{x^{2}+3x-10}{10x^{3}y^{3}}.

$$\frac{\left(x^{2}-5x+6\right)\times 10x^{3}y^{3}}{6xy^{3}\left(x^{2}+3x-10\right)}$$

Cancel out 2xy^{3} in both numerator and denominator.

$$\frac{5x^{2}\left(x^{2}-5x+6\right)}{3\left(x^{2}+3x-10\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

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

Expand the expression.

$$\frac{5x^{3}-15x^{2}}{3x+15}$$