a.
` (3m-5)/(m-1) + (2m-5)/(2-m) = 1`
`⇔ \frac{(3m-5)(2-m)+(2m-5)(m-1)}{(m-1)(2-m)}=1`
`⇔ (3m-5)(2-m)+(2m-5)(m-1)=(m-1)(2-m)`
`⇔ -3m^2-10+11m+2m^2+5-7m=-m^2-2+3m`
`⇔ -m^2-5+4m=-m^2-2+3m`
`⇔ m-3=0`
`⇔ m=3`
b.
`(9m-7)/(3m-2) + (5-4m)/(2m-3) = 1`
`⇔ \frac{(9m-7)(2m-3)+(5-4m)(3m-2)}{(3m-2)(2m-3)}=1`
`⇔ (9m-7)(2m-3)+(5-4m)(3m-2)=(3m-2)(2m-3)`
`⇔ 18m^2+21-41m-12m^2-10+23m=6m^2+6-13m`
`⇔ 11-18m=6-13m`
`⇔ 13m-18m=6-11`
`⇔ -5m=-5`
`⇔ m=1`
c.
` (2m-9)/(2m-5) -(3m)/(2-3m) -1 = 1`
`⇔ \frac{(2m-9)(2-3m)-3m(2m-5)}{(2m-5)(2-3m)}=2`
`⇔ (2m-9)(2-3m)-3m(2m-5)=2(2m-5)(2-3m)`
`⇔ -6m^2-18+31m-6m^2+15m=-12m^2-20+38m`
`⇔ 2+8m=0`
`⇔ 8m=-2`
`⇔ m= -1/4`
d.
` (m-3)/(m+3) - (1-3m)/(1+3m) -1 = 1`
`⇔ \frac{(m-3)(1+3m)-(1-3m)(m+3)}{(m+3)(1+3m)}=2`
`⇔ (m-3)(1+3m)+(3m-1)(m+3)=2(m+3)(1+3m) `
`⇔ 3m^2-3-8m+3m^2-3+8m=6m^2+6+20m`
`⇔ 12+20m=0`
`⇔ 20m=-12`
`⇔ m=-3/5`
