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Anon25 [30]
4 years ago
8

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

Mathematics
1 answer:
Slav-nsk [51]4 years ago
4 0
\frac{2m}{2m+3} - \frac{2m}{2m-3} =1 \\  \frac{2m(2m-3)-2m(2m+3)}{4m^2-9} =1 \\  \frac{4m^2-6m-4m^2-6m}{4m^2-9} =1 \\  \frac{-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, \frac{2(0.6213)}{2(0.6213)+3} - \frac{2(0.6213)}{2(0.6213)-3} \\  \frac{1.2426}{4.2426} - \frac{1.2426}{-1.7574} =0.2929+0.7071=1
For m = -3.6213, \frac{2(-3.6213)}{2(-3.6213)+3} - \frac{2(-3.6213)}{2(-3.6213)-3} \\ \frac{-7.2426}{-4.2426} - \frac{-7.2426}{-10.2426} =1.7071-0.7071=1
Therefore, the equation has no extraneous solution.
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