Cái này bạn áp dụng tính chất 1 của tỉ lệ thức là ra ngay mà!
Hai tỉ số bằng nhau khi tích 2 ngoại tỉ bằng tích 2 trung tỉ.
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) \(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\)
\(\Leftrightarrow\left(x-1\right)\left(x+3\right)=\left(x-2\right)\left(x+2\right)\)
\(\Leftrightarrow\left(x-1\right)x+\left(x-1\right).3=\left(x-2\right)x+\left(x-2\right).2\)
\(\Leftrightarrow x^2-x+3x-3=x^2-2x+2x-4\)
\(\Leftrightarrow x^2+2x-3=x^2-4\)
\(\Leftrightarrow x^2+2x-3+4-x^2=0\)
\(\Leftrightarrow2x-3+4=0\)
\(\Leftrightarrow2x=-1\)
\(\Rightarrow x=\dfrac{-1}{2}\)
Chẳng biết có đúng không...
