Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 2x^2 + 14x + 8.$ Find the quadratic whose roots are 1/(a + 1) and 1/(b + 1).
Rearrange as
x^2 +19x + 5 = 0
By Vieta .....
a + b = - 19
ab = 5
1/ ( a + 1) + 1 / (b + 1) =
[ (a + b) + 2 ] / [ ab + (a + b) + 1 ] =
[ -19 + 2 ] / [ 5 - 19 + 1 ] =
-17 / - 13 =
17 / 13
+269 
