a,
$3m(3mx-1)= 5(5x-1)$
$\Leftrightarrow 9m^2x-3m= 25x-5$
$\Leftrightarrow (9m^2-25)x= 3m-5$
$\Leftrightarrow [(3m-5)(3m+5)]x= 3m-5$ (*)
- Nếu $(3m-5)(3m+5) \neq 0 \Leftrightarrow m \neq \pm \frac{5}{3}$:
(*) $\Leftrightarrow x= \frac{3m-5}{(3m-5)(3m+5)}= \frac{1}{3m+5}$
- Nếu $(3m-5)(3m+5)= 0 \Leftrightarrow m=\frac{5}{3}$ hoặc $m= -\frac{5}{3}$:
+ Khi $m= \frac{5}{3}$:
(*) $\Leftrightarrow 0x= 0$ (vô số nghiệm)
+ Khi $m= -\frac{5}{3}$:
(*) $\Leftrightarrow 0x= -10$ (vô nghiệm)
Vậy:
Khi $m \neq \pm \frac{5}{3}; S= \{ \frac{1}{3m+5} \}$
Khi $m= \frac{5}{3}; S= R$
Khi $m= -\frac{5}{3}; S= \{ \varnothing \}$
b,
$(5x-m)m= 3(5m-3)$
$\Leftrightarrow 5mx= m^2 + 15m - 9$ (*)
- Khi $m \neq 0$:
(*) $\Leftrightarrow x= \frac{m^2 + 15m-9}{5m}$
- Khi $m = 0$:
(*) $\Leftrightarrow 0x= -9$ (vô nghiệm)
Vậy:
Khi $m \neq 0; S= \{ \frac{m^2 + 15m - 9}{5m} \}$
Khi $m= 0; S= \{ \varnothing \}$
