Question

Which solution to the equation StartFraction 3 Over 2 g + 8 EndFraction = StartFraction g + 2 Over g squared minus 16 EndFraction is extraneous?

g = –4
g = –4 and g = 16
neither g = –4 nor g = 16
g = 16

Answer 1

First note the expression is undefined at g = 4 and g = −4 (denominators 2g+8 and g^2−16 vanish there), so those cannot be solutions.

Solve:
3/(2g+8) = (g+2)/(g^2−16) = (g+2)/((g−4)(g+4))
Multiply by 2(g+4)(g−4):
3(g−4) = 2(g+2)
3g−12 = 2g+4
g = 16

g = 16 is allowed and satisfies the original equation. g = −4 is not a solution (it makes the denominators zero), so it is not an extraneous root produced by solving — it is simply excluded. Therefore no solved solution is extraneous.

Answer: neither g = −4 nor g = 16.