c: \(\dfrac{x+1}{-5}=\dfrac{-20}{x+1}\)(Điều kiện: \(x\ne-1\))
=>\(\left(x+1\right)^2=\left(-20\right)\cdot\left(-5\right)=100\)
=>\(\left[{}\begin{matrix}x+1=10\\x+1=-10\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=9\left(nhận\right)\\x=-11\left(nhận\right)\end{matrix}\right.\)
d: \(\dfrac{-4}{5}-\left(x+\dfrac{1}{2}\right)=\dfrac{1}{-5}-\dfrac{15}{10}\)
=>\(\dfrac{-4}{5}-x-\dfrac{1}{2}=\dfrac{-1}{5}-\dfrac{15}{10}\)
=>\(\dfrac{-13}{10}-x=\dfrac{-17}{10}\)
=>\(x=\dfrac{-13}{10}+\dfrac{17}{10}=\dfrac{4}{10}=\dfrac{2}{5}\)
d:
ĐKXĐ: x<>-1
\(-\dfrac{195}{13}=\dfrac{30}{x+1}=\dfrac{y^2}{-15}\)
=>\(\dfrac{30}{x+1}=\dfrac{y^2}{-15}=-15\)
=>\(\left\{{}\begin{matrix}x+1=\dfrac{30}{-15}=-2\\y^2=\left(-15\right)\cdot\left(-15\right)=225\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-3\left(nhận\right)\\y\in\left\{15;-15\right\}\end{matrix}\right.\)
e: \(x+\dfrac{1}{5}=\dfrac{4}{-10}-\dfrac{3}{2}\)
=>\(x+\dfrac{1}{5}=\dfrac{-2}{5}-\dfrac{3}{2}\)
=>\(x=\dfrac{-2}{5}-\dfrac{3}{2}-\dfrac{1}{5}=\dfrac{-3}{2}-\dfrac{3}{5}=\dfrac{-21}{10}\)
c.
\(\dfrac{x+1}{-5}=\dfrac{-20}{x+1}\)
\(\Rightarrow\left(x+1\right)^2=-20.\left(-5\right)\)
\(\Leftrightarrow\left(x+1\right)^2=100\)
\(\Rightarrow x+1=10\) hoặc \(x+1=-10\)
\(\Rightarrow x=9\) hoặc \(x=-11\)
d.
\(-\dfrac{4}{5}-\left(x+\dfrac{1}{2}\right)=\dfrac{1}{-5}-\dfrac{15}{10}\)
\(\Rightarrow-\dfrac{4}{5}-\left(x+\dfrac{1}{2}\right)=-\dfrac{17}{10}\)
\(\Rightarrow x+\dfrac{1}{2}=-\dfrac{4}{5}+\dfrac{17}{10}\)
\(\Rightarrow x+\dfrac{1}{2}=\dfrac{9}{10}\)
\(\Rightarrow x=\dfrac{9}{10}-\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{2}{5}\)
d.
\(\dfrac{-195}{13}=\dfrac{30}{x+1}=\dfrac{y^2}{-15}\)
\(\Rightarrow-15=\dfrac{30}{x+1}=\dfrac{y^2}{-15}\)
\(\Rightarrow\left\{{}\begin{matrix}x+1=30:\left(-15\right)\\y^2=-15.\left(-15\right)\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x+1=-2\\y^2=15^2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=-3\\y=\pm15\end{matrix}\right.\)
e.
\(x+\dfrac{1}{5}=\dfrac{4}{-10}-\dfrac{3}{2}\)
\(x+\dfrac{1}{5}=-\dfrac{2}{5}-\dfrac{3}{2}\)
\(x+\dfrac{1}{5}=-\dfrac{19}{10}\)
\(x=-\dfrac{19}{10}-\dfrac{1}{5}\)
\(x=-\dfrac{21}{10}\)