Suppose that a(x+b(x+3))=2(x+6) for all real values of x, find a+b. I have tried subsituting y for x+3 and solving that way but I could not find a solution. Could someone point me in the right direction? Thanks!
+2666 Simplify:
\(a(x+b(x+3)) = 2(x+6)\)
\(a(x+bx+3b) = 2x + 12\)
\(ax+abx+3ab = 2x + 12\)
Equate coefficicents:
\(ab = 4\)
\(a + ab = 2\)
Solving this system, we find \(a = -2\) and \(b = -2\) so \(a + b = \color{brown}\boxed{-4}\)
