Question

giải giùm mik pt này mik c.on nhiều nhiều

\(\dfrac{2x-5}{x-2}-\dfrac{3x-5}{x-1}=-1\)

Answer 1

ĐKXĐ: \(\left\{{}\begin{matrix}x-2\ne0\\x-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne2\\x\ne1\end{matrix}\right.\)

Pt \(\Leftrightarrow\dfrac{\left(2x-5\right).\left(x-1\right)}{\left(x-2\right).\left(x-1\right)}-\dfrac{\left(3x-5\right).\left(x-2\right)}{\left(x-2\right).\left(x-1\right)}=\dfrac{\left(x-2\right).\left(x-1\right)}{\left(x-2\right).\left(x-1\right)}\)

\(\Leftrightarrow2x^2-2x-5x+5-3x^2-6x-5x+10=x^2-2x-x+2\)

\(\Leftrightarrow2x^2-3x^2-x^2-2x-5x-6x-5x+2x+x=2-10-5\)

\(\Leftrightarrow15x=13\)

\(\Leftrightarrow x=\dfrac{13}{15}\left(TM\right)\)

Vậy nghiệm của pt là ​\(x=\dfrac{13}{15}\)

Answer 2

\(\dfrac{2x-5}{x-2}-\dfrac{3x-5}{x-1}=-1\left(ĐKXĐ:x\ne1,2\right)\)

\(\Rightarrow\left(2x-5\right)\left(x-1\right)-\left(3x-5\right)\left(x-2\right)=-\left(x-1\right)\left(x-2\right)\)

\(\Leftrightarrow2x^2-7x+5-3x^2+11x-10=-x^2+3x-2\)

\(\Leftrightarrow x=3\)

vậy phương trình có tập nghiệm là S={3}