\(\dfrac{7}{x-1}=\dfrac{5}{x-4}\left(x\ne1;4\right)\)
\(\Leftrightarrow\dfrac{7\left(x-4\right)}{\left(x-1\right)\left(x-4\right)}=\dfrac{5\left(x-1\right)}{\left(x-1\right)\left(x-4\right)}\)
\(\Leftrightarrow7x-28=5x-5\)
\(\Leftrightarrow7x-5x=-5+28\)
\(\Leftrightarrow2x=23\)
\(\Leftrightarrow x=\dfrac{23}{2}\left(Thoaman\right)\)
\(\dfrac{7}{x-1}=\dfrac{5}{x-4}\)
\(\Leftrightarrow7\left(x-4\right)-5\left(x-1\right)=0\)
\(\Leftrightarrow7x-28-5x+5=0\)
\(\Leftrightarrow2x=23\)
\(\Leftrightarrow x=\dfrac{23}{2}\)
\(\dfrac{7}{x-1}=\dfrac{5}{x-4}\)
\(\Leftrightarrow7\left(x-4\right)=5\left(x-1\right)\)
\(\Leftrightarrow7x-28=5x-5\)
\(\Leftrightarrow7x-5x=-5+28\)
\(\Leftrightarrow2x=23\)
\(\Leftrightarrow x=\dfrac{23}{2}\)
\(\dfrac{7}{x-1}=\dfrac{5}{x-4}\text{ĐKXĐ}:x\ne1;4\)
\(\Leftrightarrow\dfrac{7\left(x-4\right)}{\left(x-1\right)\left(x-4\right)}=\dfrac{5\left(x-1\right)}{\left(x-1\right)\left(x-4\right)}MTC:\left(x-1\right)\left(x-4\right)\)
\(\Rightarrow7x-28=5x-5\)
\(\Leftrightarrow7x-28-5x+5=0\)
\(\Leftrightarrow2x-23=0\)
\(\Leftrightarrow2x=23\)
\(\Leftrightarrow x=\dfrac{23}{2}\left(\text{nhận}\right)\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{\dfrac{23}{2}\right\}\)