Solve 2x(x+6)^7-x^2(4)(x+6)/(x+6)^8

$$\frac { 2 x ( x + 6 ) ^ { 7 } - x ^ { 2 } ( 4 ) ( x + 6 ) } { ( x + 6 ) ^ { 8 } }$$

Evaluate

$$\frac{2x\left(\left(x+6\right)^{6}-2x\right)}{\left(x+6\right)^{7}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{2x\left(x+6\right)\left(x^{6}+36x^{5}+540x^{4}+4320x^{3}+19440x^{2}+46654x+46656\right)}{\left(x+6\right)^{8}}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{2x\left(x^{6}+36x^{5}+540x^{4}+4320x^{3}+19440x^{2}+46654x+46656\right)}{\left(x+6\right)^{7}}$$

Expand the expression.

$$\frac{2x^{7}+72x^{6}+1080x^{5}+8640x^{4}+38880x^{3}+93308x^{2}+93312x}{x^{7}+42x^{6}+756x^{5}+7560x^{4}+45360x^{3}+163296x^{2}+326592x+279936}$$

Expand

$$\frac{2\left(x^{7}+36x^{6}+540x^{5}+4320x^{4}+19440x^{3}+46654x^{2}+46656x\right)}{\left(x+6\right)^{7}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{2x\left(x+6\right)\left(x^{6}+36x^{5}+540x^{4}+4320x^{3}+19440x^{2}+46654x+46656\right)}{\left(x+6\right)^{8}}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{2x\left(x^{6}+36x^{5}+540x^{4}+4320x^{3}+19440x^{2}+46654x+46656\right)}{\left(x+6\right)^{7}}$$

Expand the expression.

$$\frac{2x^{7}+72x^{6}+1080x^{5}+8640x^{4}+38880x^{3}+93308x^{2}+93312x}{x^{7}+42x^{6}+756x^{5}+7560x^{4}+45360x^{3}+163296x^{2}+326592x+279936}$$