Solve 2-18w^2/3w^3-8w-33w^2-7w-6/12^2+80-28

$$\frac{ 2-18 { w }^{ 2 } }{ 3 { w }^{ 3 } -8w-3 } \frac{ 3 { w }^{ 2 } -7w-6 }{ { 12 }^{ 2 } +80-28 }$$

Evaluate

$$\frac{\left(w-3\right)\left(3w+2\right)\left(1-9w^{2}\right)}{98\left(3w^{3}-8w-3\right)}$$

Short Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{2-18w^{2}}{3w^{3}-8w-3}\times \frac{3w^{2}-7w-6}{144+80-28}$$

Add 144 and 80 to get 224.

$$\frac{2-18w^{2}}{3w^{3}-8w-3}\times \frac{3w^{2}-7w-6}{224-28}$$

Subtract 28 from 224 to get 196.

$$\frac{2-18w^{2}}{3w^{3}-8w-3}\times \frac{3w^{2}-7w-6}{196}$$

Multiply \frac{2-18w^{2}}{3w^{3}-8w-3} times \frac{3w^{2}-7w-6}{196} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2-18w^{2}\right)\left(3w^{2}-7w-6\right)}{\left(3w^{3}-8w-3\right)\times 196}$$

Factor the expressions that are not already factored.

$$\frac{2\left(w-3\right)\left(-3w-1\right)\left(3w-1\right)\left(3w+2\right)}{196\left(3w^{3}-8w-3\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(w-3\right)\left(-3w-1\right)\left(3w-1\right)\left(3w+2\right)}{98\left(3w^{3}-8w-3\right)}$$

Expand the expression.

$$\frac{-27w^{4}+63w^{3}+57w^{2}-7w-6}{294w^{3}-784w-294}$$

Expand

$$-\frac{27w^{4}-63w^{3}-57w^{2}+7w+6}{98\left(3w^{3}-8w-3\right)}$$

Short Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{2-18w^{2}}{3w^{3}-8w-3}\times \frac{3w^{2}-7w-6}{144+80-28}$$

Add 144 and 80 to get 224.

$$\frac{2-18w^{2}}{3w^{3}-8w-3}\times \frac{3w^{2}-7w-6}{224-28}$$

Subtract 28 from 224 to get 196.

$$\frac{2-18w^{2}}{3w^{3}-8w-3}\times \frac{3w^{2}-7w-6}{196}$$

Multiply \frac{2-18w^{2}}{3w^{3}-8w-3} times \frac{3w^{2}-7w-6}{196} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2-18w^{2}\right)\left(3w^{2}-7w-6\right)}{\left(3w^{3}-8w-3\right)\times 196}$$

Factor the expressions that are not already factored.

$$\frac{2\left(w-3\right)\left(-3w-1\right)\left(3w-1\right)\left(3w+2\right)}{196\left(3w^{3}-8w-3\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(w-3\right)\left(-3w-1\right)\left(3w-1\right)\left(3w+2\right)}{98\left(3w^{3}-8w-3\right)}$$

Expand the expression.

$$\frac{-27w^{4}+63w^{3}+57w^{2}-7w-6}{294w^{3}-784w-294}$$