a. \(\frac{x-1}{x+5}=\frac{6}{7}\)
⇒(x-1).7 = (x+5).6
⇒7x-7 = 6x-30
⇒7x-7 = 6x-7+37
⇒x+6x-7 = 6x-7+37
⇒x = 37
2.
a) \(\frac{x-1}{x+5}=\frac{6}{7}\)
\(\Rightarrow\left(x-1\right).7=\left(x+5\right).6\)
\(\Rightarrow7x-7=6x+30\)
\(\Rightarrow7x-6x=30+7\)
\(\Rightarrow1x=37\)
\(\Rightarrow x=37\)
Vậy \(x=37.\)
b) \(\left(x-\frac{1}{2}\right)^2+\frac{2}{9}=\frac{2}{3}\)
\(\Rightarrow\left(x-\frac{1}{2}\right)^2=\frac{2}{3}-\frac{2}{9}\)
\(\Rightarrow\left(x-\frac{1}{2}\right)^2=\frac{4}{9}\)
\(\Rightarrow\left(x-\frac{1}{2}\right)^2=\left(\pm\frac{2}{3}\right)^2\)
\(\Rightarrow x-\frac{1}{2}=\pm\frac{2}{3}.\)
\(\Rightarrow\left[{}\begin{matrix}x-\frac{1}{2}=\frac{2}{3}\\x-\frac{1}{2}=-\frac{2}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{2}{3}+\frac{1}{2}\\x=\left(-\frac{2}{3}\right)+\frac{1}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{7}{6}\\x=-\frac{1}{6}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{7}{6};-\frac{1}{6}\right\}.\)
Chúc bạn học tốt!