Expert: Bobby Soltani - 2/4/2005

Question
given g(x)=4/x +9/(x+2) find all x that satisfy g(x)=-2

Answer
Hi Tara,

g(x) = -2 = 4/x + 9/(x+2)
we need to get a common denominator so we will multiply the first term by (x+2)/(x+2) and the second term by x/x.  This will give us the denominator of x(x+2).

-2 = (4*(x+2))/(x(x+2)) + 9x/(x(x+2))
add the numerators

-2 = (4x + 8 + 9x)/(x(x+2))
-2 = (13x + 8)/(x^2+2x)
multiply both sides by (x^2+2x)
-2*(x^2+2x) = 13x + 8
-2x^2 - 4x = 13x + 8
subtract 13x + 8 from both sides

-2x^2 - 17x - 8 = 0

now we can use the quadradic equation with a = -2, b = -17, c = -8.

When I do this, I get x = -1/2 and x = -8.

Let me know if you have questions.

Bobby