Limit Substitution

Just letting a value equal to a more complex value temporarily

Example

${\lim }_{x\to 0}\frac{(x+8{)}^{\frac{1}{3}}-2}{x}$ let $u=(x+8{)}^{1/3}$ $u^3=x+8$ ${\lim }_{u\to 2}\frac{u-2}{u^3-8}$ ${\lim }_{u\to 2}\frac{u-2}{(u-2)(u^2+2u+4)}$ ${\lim }_{u\to 2}\frac{1}{(u^2+2u+4)}$ $\frac{1}{(2{)}^2+2(2)+4}$ $\frac{1}{12}$