Question

Lim (1/4+1/x)/4+x
X→-4

Answer 1

`\displaystyle \lim_(x\to -4)~\cfrac{~~ (1 )/(4 )+(1)/(x) ~~}{4+x} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ (1 )/(4 )+(1)/(x) ~~}{4+x}\implies \cfrac{~~ (4+x)/(4x) ~~}{4+x}\implies \cfrac{~~ (4+x)/(4x) ~~}{(4+x)/(1)}\implies \cfrac{4+x}{4x}\cdot \cfrac{1}{4+x}\implies \cfrac{1}{4x} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_(x\to -4)~\cfrac{1}{4x}\implies \cfrac{1}{4(-4)}\implies -\cfrac{1}{16}`