<PRE><B>Question 30737</B>

   14 over b-6 = 1/2 + 6 over b-8

or it is written as 


   14 / b-6 = 1/2 + 6 / b-8

on taking LCM on RHS we get..

14 / b-6 =  ( b-8 + 12) / 2(b-8)

14 / b-6 =   b + 4 / 2b -16 

cross multiply and we get..

14(2b-16) = (b+4)(b-6)

solving brackets on both side give us ...

28b - 224 = b^2 - 2b -24

putting together the like variables ,,,

0 = b^2 - 2b -28b -24 + 224

0 =  b^2 - 30b + 200

Here you must know how we make factors i.e. splitting of the middle term...if you might not know then please contact me again and I will explain to you...

0 = b^2 -( 20 -10)b + 200

0 = b^2 - 20b - 10b + 200

taking common from first two i.e. b^2 - 20b and last two i.e. 10b + 200
variables...we get 


0 = b(b-20) -10(b-20)

0= (b-10)(b-20)

hope this will help you 

Please feel free to revert back for any further queries.</PRE>