Solve 3x^2-14x+8/2x^2-3x-20div9-x^2/-x^2+x+12

$$\frac { 3 x ^ { 2 } - 14 x + 8 } { 2 x ^ { 2 } - 3 x - 20 } \div \frac { 9 - x ^ { 2 } } { - x ^ { 2 } + x + 12 }$$

Evaluate

$$\frac{\left(x-4\right)\left(3x-2\right)}{\left(x-3\right)\left(2x+5\right)}$$

Short Solution Steps

Divide \frac{3x^{2}-14x+8}{2x^{2}-3x-20} by \frac{9-x^{2}}{-x^{2}+x+12} by multiplying \frac{3x^{2}-14x+8}{2x^{2}-3x-20} by the reciprocal of \frac{9-x^{2}}{-x^{2}+x+12}.

$$\frac{\left(3x^{2}-14x+8\right)\left(-x^{2}+x+12\right)}{\left(2x^{2}-3x-20\right)\left(9-x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(-x-3\right)\left(3x-2\right)\left(x-4\right)^{2}}{\left(x-4\right)\left(x-3\right)\left(-x-3\right)\left(2x+5\right)}$$

Cancel out \left(x-4\right)\left(-x-3\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(3x-2\right)}{\left(x-3\right)\left(2x+5\right)}$$

Expand the expression.

$$\frac{3x^{2}-14x+8}{2x^{2}-x-15}$$

Expand

$$-\frac{3x^{2}-14x+8}{\left(3-x\right)\left(2x+5\right)}$$

Short Solution Steps

Divide \frac{3x^{2}-14x+8}{2x^{2}-3x-20} by \frac{9-x^{2}}{-x^{2}+x+12} by multiplying \frac{3x^{2}-14x+8}{2x^{2}-3x-20} by the reciprocal of \frac{9-x^{2}}{-x^{2}+x+12}.

$$\frac{\left(3x^{2}-14x+8\right)\left(-x^{2}+x+12\right)}{\left(2x^{2}-3x-20\right)\left(9-x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(-x-3\right)\left(3x-2\right)\left(x-4\right)^{2}}{\left(x-4\right)\left(x-3\right)\left(-x-3\right)\left(2x+5\right)}$$

Cancel out \left(x-4\right)\left(-x-3\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(3x-2\right)}{\left(x-3\right)\left(2x+5\right)}$$

Expand the expression.

$$\frac{3x^{2}-14x+8}{2x^{2}-x-15}$$