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