Question

giải pt

1/ 2x-3 -3/ x (2x - 3)=5/x

Answer 1

ĐKXĐ: \(x\notin\left\{0;\frac{3}{2}\right\}\)

Ta có: \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)

\(\Leftrightarrow\frac{x}{x\left(2x-3\right)}-\frac{3}{x\left(2x-3\right)}-\frac{5\left(2x-3\right)}{x\left(2x-3\right)}=0\)

\(\Leftrightarrow x-3-5\left(2x-3\right)=0\)

\(\Leftrightarrow x-3-10x+15=0\)

\(\Leftrightarrow-9x+12=0\)

\(\Leftrightarrow-9x=-12\)

hay \(x=\frac{4}{3}\)(tm)

Vậy: \(x=\frac{4}{3}\)

Answer 2

\(\frac{1}{2x}-3-\frac{3}{x}\left(2x-3\right)=\frac{5}{x}\)

\(\frac{1}{2x}-3-\frac{3\left(2x-3\right)}{x}=\frac{5}{x}\)

\(\frac{1}{2x}-\frac{3\left(2x-3\right)}{x}-3=\frac{5}{x}\)

\(x=\frac{1}{2}\)