SOLUTION: 9*(x+2/x+3)^2-6*(x+2/x+3)+1=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 9*(x+2/x+3)^2-6*(x+2/x+3)+1=0      Log On


   

Question 191816: 9*(x+2/x+3)^2-6*(x+2/x+3)+1=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x???
9%2A%28%28x%2B2%29%2F%28x%2B3%29%29%5E2-6%2A%28%28x%2B2%29%2F%28x%2B3%29%29%2B1+=+0
Just to facilitate solving, let's temporarily substitute: z+=+%28%28x%2B2%29%2F%28x%2B3%29%29, so now we have:
9z%5E2-6z%2B1+=+0 Factor this quadratic equation.
%283z-1%29%283z-1%29+=+0 Apply the zero product rule:
3z-1+=+0, so...
3z+=+1 and...
z+=+1%2F3 Now re-substitute z+=+%28%28x%2B2%29%2F%28x%2B3%29%29 to get:
%28%28x%2B2%29%2F%28x%2B3%29%29+=+1%2F3 Cross multiply.
3%28x%2B2%29+=+%28x%2B3%29 Simplify.
3x%2B6+=+x%2B3 Subtract x from both sides.
2x%2B6+=+3 Subtract 6 from both sides.
2x+=+-3 Finally, divide both sides by 2.
highlight%28x+=+-3%2F2%29
Check:
9%2A%28%28x%2B2%29%2F%28x%2B3%29%29%5E2-6%2A%28%28x%2B3%29%2F%28x%2B2%29%29%2B1+=+0 Substitute x+=+-3%2F2

9%2A%28%281%2F2%29%2F%283%2F2%29%29%5E2-6%2A%28%281%2F2%29%2F%283%2F2%29%29%2B1+=+0 Simplify:
9%2A%281%2F3%29%5E2-6%2A%281%2F3%29%2B1+=+0
9%2A%281%2F9%29-6%2A%281%2F3%29%2B1+=+0
1-2%2B1+=+0
0+=+0 OK!