\(a)\dfrac{x+5}{x-3}+2=\dfrac{2}{x-3}\left(x\ne3\right)\)
`<=>` \(\dfrac{x+5}{x-3}+\dfrac{2\left(x-3\right)}{x-3}=\dfrac{2}{x-3}\)
`<=>` \(x+5+2\left(x-3\right)=2\)
`<=>` `x+5+2x-6=2`
`<=>x+2x=2-5+6`
`<=>3x=3`
`<=>x=1`
Vậy phương trình có nghiệm `x=1`
\(b)\dfrac{2}{x-2}+\dfrac{3}{x-3}=\dfrac{3x-20}{\left(x-2\right)\left(x-3\right)}\left(x\ne2;3\right)\)
`<=>` \(\dfrac{2\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}+\dfrac{3\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}=\dfrac{3x-20}{\left(x-2\right)\left(x-3\right)}\)
`<=>` \(2\left(x-3\right)+3\left(x-2\right)=3x-20\)
`<=>` `2x-6+3x-6=3x-20`
`<=>` `2x+3x-3x=-20+6+6`
`<=>` `2x=-8`
`<=>` `x=-4`
Vậy phương trình có nghiệm `x=-4`
\(c)\dfrac{3}{x-2}+\dfrac{2}{x+1}=\dfrac{2x+5}{\left(x-2\right)\left(x+1\right)}\left(x\ne2;-1\right)\)
`<=>` \(\dfrac{3\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\dfrac{2\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}=\dfrac{2x+5}{\left(x-2\right)\left(x+1\right)}\)
`<=>` `3(x+1)+2(x-2)=2x+5`
`<=>` `3x+3+2x-4=2x+5`
`<=>` `3x+2x-2x=5-3+4`
`<=>` `3x=6`
`<=>` `x=2` (không thỏa mãn)
`<=>` Vô nghiệm
Vậy phương trình vô nghiệm.
a) \(\dfrac{x+5}{x-3}+2=\dfrac{2}{x-3}\left(x\ne3\right)\)
\(\Leftrightarrow\dfrac{x+5}{x-3}+\dfrac{2\left(x-3\right)}{x-3}=\dfrac{2}{x-3}\)
\(\Leftrightarrow x+5+2\left(x-3\right)=2\)
\(\Leftrightarrow x+5+2x-6=2\)
\(\Leftrightarrow3x-1=2\)
\(\Leftrightarrow3x=3\)
\(\Leftrightarrow x=1\left(tm\right)\)
Vậy: ...
b) \(\dfrac{2}{x-2}+\dfrac{3}{x-3}=\dfrac{3x-20}{\left(x-2\right)\left(x-3\right)}\left(x\ne2;x\ne3\right)\)
\(\Leftrightarrow\dfrac{2\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}+\dfrac{3\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}=\dfrac{3x-20}{\left(x-2\right)\left(x-3\right)}\)
\(\Leftrightarrow2\left(x-3\right)+3\left(x-2\right)=3x-20\)
\(\Leftrightarrow2x-6+3x-6=3x-20\)
\(\Leftrightarrow5x-12=3x-20\)
\(\Leftrightarrow5x-3x=-20+12\)
\(\Leftrightarrow2x=-8\)
\(\Leftrightarrow x=-4\left(tm\right)\)
Vậy: ...
c) \(\dfrac{3}{x-2}+\dfrac{2}{x+1}=\dfrac{2x+5}{\left(x-2\right)\left(x+1\right)}\left(x\ne2;x\ne-1\right)\)
\(\Leftrightarrow\dfrac{3\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}+\dfrac{2\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}=\dfrac{2x+5}{\left(x-2\right)\left(x+1\right)}\)
\(\Leftrightarrow3\left(x+1\right)+2\left(x-2\right)=2x+5\)
\(\Leftrightarrow3x+3+2x-4=2x+5\)
\(\Leftrightarrow5x-1=2x+5\)
\(\Leftrightarrow5x-2x=5+1\)
\(\Leftrightarrow3x=6\)
\(\Leftrightarrow x=2\left(ktm\right)\)
Vậy pt vô nghiệm
