Solve 2x^3+18^2/2x^3-8x^2div2/7x-21

$$\frac { 2 x ^ { 3 } + 18 ^ { 2 } } { 2 x ^ { 3 } - 8 x ^ { 2 } } \div \frac { 2 } { 7 x - 21 }$$

Evaluate

$$\frac{7\left(x-3\right)\left(x^{3}+162\right)}{2\left(x-4\right)x^{2}}$$

Short Solution Steps

Divide \frac{2x^{3}+18^{2}}{2x^{3}-8x^{2}} by \frac{2}{7x-21} by multiplying \frac{2x^{3}+18^{2}}{2x^{3}-8x^{2}} by the reciprocal of \frac{2}{7x-21}.

$$\frac{\left(2x^{3}+18^{2}\right)\left(7x-21\right)}{\left(2x^{3}-8x^{2}\right)\times 2}$$

Calculate 18 to the power of 2 and get 324.

$$\frac{\left(2x^{3}+324\right)\left(7x-21\right)}{\left(2x^{3}-8x^{2}\right)\times 2}$$

Factor the expressions that are not already factored.

$$\frac{2\times 7\left(x-3\right)\left(x^{3}+162\right)}{2^{2}\left(x-4\right)x^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7\left(x-3\right)\left(x^{3}+162\right)}{2\left(x-4\right)x^{2}}$$

Expand the expression.

$$\frac{7x^{4}-21x^{3}+1134x-3402}{2x^{3}-8x^{2}}$$

Expand

$$\frac{7\left(x^{4}-3x^{3}+162x-486\right)}{2\left(x^{3}-4x^{2}\right)}$$

Short Solution Steps

Divide \frac{2x^{3}+18^{2}}{2x^{3}-8x^{2}} by \frac{2}{7x-21} by multiplying \frac{2x^{3}+18^{2}}{2x^{3}-8x^{2}} by the reciprocal of \frac{2}{7x-21}.

$$\frac{\left(2x^{3}+18^{2}\right)\left(7x-21\right)}{\left(2x^{3}-8x^{2}\right)\times 2}$$

Calculate 18 to the power of 2 and get 324.

$$\frac{\left(2x^{3}+324\right)\left(7x-21\right)}{\left(2x^{3}-8x^{2}\right)\times 2}$$

Factor the expressions that are not already factored.

$$\frac{2\times 7\left(x-3\right)\left(x^{3}+162\right)}{2^{2}\left(x-4\right)x^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7\left(x-3\right)\left(x^{3}+162\right)}{2\left(x-4\right)x^{2}}$$

Expand the expression.

$$\frac{7x^{4}-21x^{3}+1134x-3402}{2x^{3}-8x^{2}}$$