Question

What is the solution to the equation 3/2g+8 = g+2/g^2 -16 is extraneous

Answer 1

g = 16

Explanation:

`Domain:\\\\2g+8\\eq0\ \wedge\ g^2-16\\eq0\\\\g\\eq-4\ \wedge\ g\\eq4\\====================\\\\(3)/(2g+8)=(g+2)/(g^2-16)\qquad\text{cross multiply}\\\\3(g^2-16)=(2g+8)(g+2)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\text{and}\ FOIL:\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3)(g^2)+(3)(-16)=(2g)(g)+(2g)(2)+(8)(g)+(8)(2)\\\\3g^2-48=2g^2+4g+8g+16\qquad\text{subtract}\ 2g^2\ \text{from both sides}\\\\g^2-48=12g+16\qquad\text{subtract}\ 12g\ \text{and}\ 16\ \text{from both sides}`

`g^2-12g-64=0\\\\g^2+4g-16g-64=0\\\\g(g+4)-16(g+4)=0\\\\(g+4)(g-16)=0\iff g+4=0\ \vee\ g-16=0\\\\g+4=0\qquad\text{subtract 4 from both sides}\\g=-4\\otin D\\\\g-16=0\qquad\text{add 16 to both sides}\\g=16\in D`