Tìm x biết x-3/x+5=5/7

a) \(\dfrac{x-3}{x+5}=\dfrac{5}{7}\)

\(\Leftrightarrow7\left(x-3\right)=5\left(x+5\right)\)

\(\Leftrightarrow7x-21=5x+25\)

\(\Leftrightarrow7x-5x=25+21\)

\(\Leftrightarrow2x=46\)

\(\Rightarrow x=\dfrac{46}{2}=23\)

b) \(\dfrac{7}{x-1}=\dfrac{x+1}{9}\)

\(\Leftrightarrow7.9=\left(x+1\right)\left(x-1\right)\)

\(\Leftrightarrow63=\left(x+1\right)x-\left(x+1\right)\)

\(\Leftrightarrow63=x^2+x-x-1\)

\(\Leftrightarrow63=x^2-1\)

\(\Leftrightarrow63+1=x^2\)

\(\Rightarrow64=x^2\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

c) \(\dfrac{x+4}{20}=\dfrac{5}{x+4}\)

\(\Leftrightarrow\left(x+4\right)^2=5.20\)

\(\Leftrightarrow\left(x+4\right)^2=100=10^2=\left(-10\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x+4=10\\x+4=-10\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=6\\x=-14\end{matrix}\right.\)

d) \(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\)

\(\Leftrightarrow\left(x-1\right)\left(x+3\right)=\left(x-2\right)\left(x+2\right)\)

\(\Leftrightarrow\left(x-1\right)x+\left(x-1\right).3=\left(x-2\right)x+\left(x-2\right).2\)

\(\Leftrightarrow x^2-x+3x-3=x^2-2x+2x-4\)

\(\Leftrightarrow x^2+2x-3=x^2-4\)

\(\Leftrightarrow x^2+2x-3+4-x^2=0\)

\(\Leftrightarrow2x-3+4=0\)

\(\Leftrightarrow2x=-1\)

\(\Rightarrow x=\dfrac{-1}{2}\)

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