Giải :
\(a,ĐK:\left\{{}\begin{matrix}x\ne\dfrac{3}{2}\\x\ne\dfrac{5}{3}\end{matrix}\right.\\ \Leftrightarrow\dfrac{4\left(3x-5\right)}{\left(2x-3\right)\left(3x-5\right)}-\dfrac{7\left(2x-3\right)}{\left(2x-3\right)\left(3x-5\right)}=0\\ \Leftrightarrow4.\left(3x-5\right)-7.\left(2x-3\right)=0\\ \Leftrightarrow12x-20-14x+21=0\\ \Leftrightarrow-2x+1=0\\ \Leftrightarrow x=\dfrac{1}{2}\left(t/m\right)\)
Vậy \(x=\dfrac{1}{2}\)
\(b,ĐK:\left\{{}\begin{matrix}x\ne\dfrac{3}{2}\\x\ne-\dfrac{3}{2}\end{matrix}\right.\\ \Leftrightarrow\dfrac{4}{2x-3}+\dfrac{4x}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{1}{2x+3}\\ \Leftrightarrow\dfrac{4.\left(2x+3\right)+4x}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{2x-3}{\left(2x+3\right)\left(2x-3\right)}\\ \Leftrightarrow8x+12+4x=2x-3\\ \Leftrightarrow12x+12-2x+3=0\\ \Leftrightarrow10x=-15\\ \Leftrightarrow x=-\dfrac{3}{2}\left(kot/m\right)\)
Vậy phương trình vô nghiệm
a: =>4(3x-5)-7(2x-3)=0
=>12x-20-14x+21=0
=>1-2x=0
=>x=1/2
b: =>4(2x+3)+4x=2x-3
=>8x+12+4x=2x-3
=>12x+12=2x-3
=>10x=-15
=>x=-3/2(loại)
