Question

\(\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\)

Answer 1

\(\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\)

<=>\(\frac{x+10}{x\left(x+10\right)}+\frac{x}{x\left(x+10\right)}=\frac{1}{12}\)ĐKXĐ:\(x\pm-10\)

<=>\(\frac{2x+10}{x\left(x+10\right)}=\frac{1}{12}\)

<=>24x+120=x²+10x

<=>x²-14x-120=0

<=>x²-20x+6x-120=0

<=>x(x-20)+6(x-20)=0

<=>(x+6)(x-20)=0

=>\(\left[{}\begin{matrix}x+6=0< =>x=-6\left(tm\right)\\x-20=0< =>x=20\left(tm\right)\end{matrix}\right.\)

vậy pt có tập nghiệm s={-6;20}