\(\dfrac{7x+7}{x-1}=\dfrac{2}{3}\) \(\left(dkxd:x\ne1\right)\)
\(\Rightarrow3\left(7x+7\right)-2\left(x-1\right)=0\)
\(\Rightarrow21x+21-2x+2=0\)
\(\Rightarrow21x-2x=-2-21\)
\(\Rightarrow19x=-23\)
\(\Rightarrow x=-\dfrac{23}{19}\left(tmdk\right)\)
Vậy \(S=\left\{-\dfrac{23}{19}\right\}\)
\(c,\dfrac{1}{x-2}+3=\dfrac{3-x}{x-2}\left(dkxd:x\ne2\right)\)
\(\Leftrightarrow\dfrac{1}{x-2}+3-\dfrac{3-x}{x-2}=0\)
\(\Leftrightarrow\dfrac{1+3\left(x-2\right)-3+x}{x-2}=0\)
\(\Leftrightarrow1+3x-6-3+x=0\)
\(\Leftrightarrow4x=8\)
\(\Leftrightarrow x=2\left(ktmdk\right)\)
Vậy \(S=\varnothing\)
a) \(\dfrac{7x+7}{x-1}=\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{7\left(x+1\right)}{x-1}=\dfrac{2}{3}\)
\(\Leftrightarrow21\left(x+1\right)=2\left(x-1\right)\)
\(\Leftrightarrow21x+21=2x-2\)
\(\Leftrightarrow21x-2x=-2-21\)
\(\Leftrightarrow19x=-23\)
\(\Leftrightarrow x=-\dfrac{23}{19}\)
c) \(\dfrac{1}{x-2}+3=\dfrac{3-x}{x-2}\) ĐKXĐ (x≠2)
\(\Leftrightarrow\dfrac{1}{x-2}+\dfrac{3\left(x-2\right)}{x-2}=\dfrac{3-x}{x-2}\)
\(\Leftrightarrow1+3\left(x-2\right)=3-x\)
\(\Leftrightarrow1+3x-6=3-x\)
\(\Leftrightarrow3x+x=3-1+6\)
\(\Leftrightarrow4x=8\)
\(\Leftrightarrow x=\dfrac{8}{4}=2\) (không thỏa mãn)
