<PRE><B>Question 30737</B>
14 over b-6 = 1/2 + 6 over b-8

14/(b-6) = 1/2 +6/(b-8)  ----(1)
Multiplying through out by 2(b-6)(b-8)(which is the lcm of the drs)
14X[2(b-8)] = (b-6)(b-8)+6X[2(b-6)]
28(b-8) = b(b-8)-6(b-8)+12(b-6)
28b-224 = b^2-8b-6b+48 +12b-72
0 = b^2-28b-8b-6b+12b+224+48-72 (grouping like terms)
0 = b^2-30b+200
That is b^2-30b+200 =0 
(b-20)(b-10) = 0  (the sum is -30 and product is +200 and therefore the quantities are -20 and -10 )
(b-20) =0 gives b = 20
(b-10) =0 gives b = 10
Answer: b = 10 and b = 20
Verification: Putting b = 10 in (1)
LHS = 14/(10-6) = 14/4 = 7/2
And RHS = 1/2+6/(10-8)
=1/2+6/2
=1/2+3
=7/2 =LHS
Putting b = 20 in (1)
LHS = 14/(20-6) = 14/14 = 1
And RHS = 1/2+6/(20-8)
=1/2+6/12
=1/2+1/2
=1 =LHS
Therefore our values are correct</PRE>