Question

2m/(2m 3)-(2m)/(2m-3)=1how many extraneous solutions does the equation have?

Answer 1

`(2m)/(2m+3) - (2m)/(2m-3) =1 \\ (2m(2m-3)-2m(2m+3))/(4m^2-9) =1 \\ (4m^2-6m-4m^2-6m)/(4m^2-9) =1 \\ (-12m)/(4m^2-9) =1 \\ -12m=4m^2-9 \\ 4m^2+12m-9=0 \\ m=0.6213 \ or \ m=-3.6213`
For m = 0.6213,
`(2(0.6213))/(2(0.6213)+3) - (2(0.6213))/(2(0.6213)-3) \\ (1.2426)/(4.2426) - (1.2426)/(-1.7574) =0.2929+0.7071=1`
For m = -3.6213,
`(2(-3.6213))/(2(-3.6213)+3) - (2(-3.6213))/(2(-3.6213)-3) \\ (-7.2426)/(-4.2426) - (-7.2426)/(-10.2426) =1.7071-0.7071=1`
Therefore, the equation has no extraneous solution.