Đáp án:

$k,$ Phương trình có nghiệm $S=$`{``-5/9``}`

$h,$ Phương trình vô nghiệm `{`$∅$`}`

$l,$  Phương trình có nghiệm $S=$`{`$3$`}`

$m,$ Phương trình có nghiệm $S=$`{`$-3$`}`

Giải thích các bước giải:

$k,$ `(3x-1)/(x-1)`$-$`(2x+5)/(x-3)`$=1$     $DKXD: x$ $\neq$ $1$$;$ $x$ $\neq$ $3$

$⇔$ `((3x-1)(x-3))/((x-1)(x-3))`$-$`((2x+5)(x-1))/((x-1)(x-3))`$=$`((x-1)(x-3))/((x-1)(x-3))`

$⇔$ $3x^2-9x-x+3-2x^2+2x-5x+5=x^2-3x-x+3$

$⇔$ $3x^2-9x-x+3-2x^2+2x-5x+5-x^2+3x+x-3=0$

$⇔$ $(3x^2-2x^2-x^2)+(-9x-x+2x-5x+3x+x)+(3+5-3)=0$

$⇔$ $-9x+5=0$

$⇔$ $-9x=-5$

$⇔$ $x$$=$`-5/9`

Vậy: phương trình có nghiệm $S=$`{``-5/9``}`

$h,$ `(x+3)/(x+1)`$+$`(x-2)/x`$=2$       $DKXD: x$ $\neq$ $-1$

$⇔$ `((x+3)x)/(x(x+1))`$+$`((x-2)(x+1))/(x(x+1))`$=$`(2x(x+1))/(x(x+1))`

$⇔$ $x^2+3x+x^2+x-2x-2=2x^2+2x$

$⇔$ $x^2+3x+x^2+x-2x-2-2x^2-2x=0$

$⇔$ $(x^2+x^2-2x^2)+(3x+x-2x-2x)-2=0$

$⇔$ $-2=0$ $($Vô lí$)$

Vậy: Phương trình vô nghiệm `{`$∅$`}`

$l,$ `2/(x+1)`$-$`1/(x-2)`$=$`(3x-11)/((x+1)(x-2))`          $DKXD: x$ $\neq$ $-1$$;$$x$ $\neq$ $2$

$⇔$`(2(x-2))/((x+1)(x-2))`$-$`(x+1)/((x+1)(x-2))`$=$`(3x-11)/((x+1)(x-2))` 

$⇔$ $2x-4-x-1=3x-11$

$⇔$ $2x-4-x-1-3x+11=0$

$⇔$ $(2x-x-3x)+(11-4-1)=0$

$⇔$ $-2x+6=0$

$⇔$ $-2x=-6$

$⇔$ $x=3$

Vậy: Phương trình có nghiệm $S=$`{`$3$`}`

$m,$`(3x-1)/(x-1)`$-$`(2x+5)/(x+3)`$+$`4/(x^2+2x-3)`$=1$     $DKXD: x$ $\neq$ $1$$;$$x$ $\neq$ $-3$

$⇔$`((3x-1)(x+3))/((x-1)(x+3))`$-$`((2x+5)(x-1))/((x-1)(x+3))`$+$`4/(x^2+3x-x-3)`$=1$

$⇔$`((3x-1)(x+3))/((x-1)(x+3))`$-$`((2x+5)(x-1))/((x-1)(x+3))`$+$`4/((x^2-x)+(3x-3))`$=$`((x-1)(x+3))/((x-1)(x+3))`

$⇔$`((3x-1)(x+3))/((x-1)(x+3))`$-$`((2x+5)(x-1))/((x-1)(x+3))`$+$`4/(x(x-1)+3(x-1))`$=$`((x-1)(x+3))/((x-1)(x+3))`

$⇔$`((3x-1)(x+3))/((x-1)(x+3))`$-$`((2x+5)(x-1))/((x-1)(x+3))`$+$`4/((x-1)(x+3))`$=$`((x-1)(x+3))/((x-1)(x+3))`

$⇔$ $3x^2+9x-x-3-(2x^2-2x+5x-5)+4=(x-1)(x+3)$

$⇔$ $3x^2+9x-x-3-2x^2+2x-5x+5+4=x^2+3x-x-3$

$⇔$ $3x^2+9x-x-3-2x^2+2x-5x+5+4-x^2-3x+x+3=0$

$⇔$ $3x^2-2x^2-x^2+9x-x+2x-5x-3x+x-3+5+4+3=0$

$⇔$ $3x+9=0$

$⇔$ $3x=-9$

$⇔$ $x=-3$

Vậy: Phương trình có nghiệm $S=$`{`$-3$`}`