a) \(\dfrac{7x-3}{x-1}=\dfrac{2}{3}\) (1)
ĐKXĐ: \(x\ne1\)
(1) \(\Leftrightarrow3\left(7x-3\right)=2\left(x-1\right)\)
\(\Leftrightarrow21x-9=2x-2\)
\(\Leftrightarrow21x-2x=-2+9\)
\(\Leftrightarrow19x=7\)
\(x=\dfrac{7}{19}\) (nhận)
Vậy \(S=\left\{\dfrac{7}{19}\right\}\)
b) \(\dfrac{x+5}{x-5}-\dfrac{x-5}{x+5}=\dfrac{20}{x^2-25}\) (2)
ĐKXĐ: \(x\ne5;x\ne-5\)
(2) \(\Leftrightarrow\left(x+5\right)^2-\left(x-5\right)^2=20\)
\(\Leftrightarrow x^2+10x+25-x^2+10x-25=20\)
\(\Leftrightarrow20x=20\)
\(\Leftrightarrow x=1\) (nhận)
Vậy \(S=\left\{1\right\}\)
c) \(\dfrac{1}{x}+\dfrac{1}{x+10}=\dfrac{1}{12}\) (3)
ĐKXĐ: \(x\ne-10;x\ne0\)
(3) \(\Leftrightarrow12\left(x+10\right)+12x=x\left(x+10\right)\)
\(\Leftrightarrow12x+120+12x=x^2+10x\)
\(\Leftrightarrow x^2+10x-12x-12x-120=0\)
\(\Leftrightarrow x^2-14x-120=0\)
\(\Leftrightarrow x^2+6x-20x-120=0\)
\(\Leftrightarrow\left(x^2+6x\right)-\left(20x-120\right)=0\)
\(\Leftrightarrow x\left(x+6\right)-20\left(x+6\right)=0\)
\(\Leftrightarrow\left(x+6\right)\left(x-20\right)=0\)
\(\Leftrightarrow x+6=0\) hoặc \(x-20=0\)
*) \(x+6=0\)
\(\Leftrightarrow x=-6\) (nhận)
*) \(x-20=0\)
\(\Leftrightarrow x=20\) (nhận)
Vậy \(S=\left\{-6;20\right\}\)
