Question

Giải các pt sau:

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

Answer 1

\(\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\)ĐKXĐ: x \(\ne\)0,x\(\ne\)-10

\(\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\Leftrightarrow\frac{12\left(x+10\right)}{12x\left(x+10\right)}+\frac{12x}{12x\left(x+10\right)}=\frac{x\left(x+10\right)}{12x\left(x+10\right)}\Rightarrow12x+120+12x=x^2+10x\Leftrightarrow x^2+10x-24x-120=0\Leftrightarrow x^2-14x-120=0\Leftrightarrow x^2-20x+6x-120=0\Leftrightarrow x\left(x-20\right)+6\left(x-20\right)\Leftrightarrow\left(x+6\right)\left(x-20\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=20\end{matrix}\right.\)Vậy S=\(\left\{-6;20\right\}\)

Answer 2

Theo mik thì chắc đảo hết phân số lại

Answer 3

+) Đkxđ :

x \(\ne\)0

x + 10 \(\ne\)0 \(\rightarrow\)x \(\ne\)-10

\(\Rightarrow\)12(x + 10) + 12 = x + 10

\(\Leftrightarrow\)12x + 120 + 12 = x + 10

\(\Leftrightarrow\) 12x + 132 = x + 10

\(\Leftrightarrow\) 12x - x = 10 - 132

\(\Leftrightarrow\) 11x = -122

\(\Leftrightarrow\) x = -11 ( TMĐK )

Vậy S = \(\left\{-11\right\}\)