Which solution to the equation 3/2g+8 g+2/g^2-16 is extraneous? a. g = –4 b. g = –4 and g = 16 c. neither g = –4 nor g = 16 d. g = 16

g = -4 is the extraneous solution.

Step-by-step explanation:

The given equation :

3 (g²-16) = ( g + 2 ) ( 2g + 8 )

3g² - 48 = 2g² + 8g + 4g + 16

( 3g² - 2g² ) = ( 8g + 4g ) + ( 16 + 48 )

g² = 12g + 64

g² - 12g - 64 = 0

g² - 16g + 4g - 64   = 0

g ( g- 16 ) + 4 ( g - 16 ) = 0

( g + 4 ) ( g - 16 ) = 0

Since ( g + 4 ) & ( g - 16 ) are zero factors

So, g = -4, 16

Now we test these solutions. for (g = -4)

L.H.S (Left Hand Side)=

R.H.S. (Right Hand Side) =

L.H.S. ≠ R.H.S. So g = ( -4) is not the answer, so g = -4 is the extraneous solution.

Now for g = 16

L.H.S.

and R.H.S.

so LHS = RHS

Therefore. g = 16 is not the extraneous solution.