SOLUTION: I need to solve the equation and I am very confused. Help!! 14 over b-6 = 1/2 + 6 over b-8 Thanks

Question 30737: I need to solve the equation and I am very confused. Help!!
14 over b-6 = 1/2 + 6 over b-8
Thanks
Found 2 solutions by sdmmadam@yahoo.com, ikdeep:
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
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
Answer by ikdeep(226) (Show Source): You can put this solution on YOUR website!

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.
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