Solve 6*limx^3-1/x^5-1=(x-1)/(x-1)

$$\frac { 6 \cdot \lim x ^ { 3 } - 1 } { x ^ { 5 } - 1 } = \frac { ( x - 1 ) } { ( x - 1 ) }$$

Solve for l

$$\left\{\begin{matrix}l=\frac{x^{5}}{6Im(x^{3})}\text{, }&Im(x^{3})\neq 0\text{ and }x\neq e^{\frac{2\pi i}{5}}\text{ and }x\neq e^{\frac{8\pi i}{5}}\text{ and }x\neq e^{\frac{6\pi i}{5}}\text{ and }x\neq e^{\frac{4\pi i}{5}}\\l\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)\left(x^{4}+x^{3}+x^{2}+x+1\right), the least common multiple of x^{5}-1,x-1.

$$6lIm(x^{3})-1=\left(x^{4}+x^{2}+x^{3}+x+1\right)\left(x-1\right)$$

Use the distributive property to multiply x^{4}+x^{2}+x^{3}+x+1 by x-1 and combine like terms.

$$6lIm(x^{3})-1=x^{5}-1$$

Add 1 to both sides.

$$6lIm(x^{3})=x^{5}-1+1$$

Add -1 and 1 to get 0.

$$6lIm(x^{3})=x^{5}$$

The equation is in standard form.

$$6Im(x^{3})l=x^{5}$$

Divide both sides by 6Im(x^{3}).

$$\frac{6Im(x^{3})l}{6Im(x^{3})}=\frac{x^{5}}{6Im(x^{3})}$$

Dividing by 6Im(x^{3}) undoes the multiplication by 6Im(x^{3}).

$$l=\frac{x^{5}}{6Im(x^{3})}$$