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If the given problem is 6x/(x-6) -4/x=24/(x^2-6x) ----(1)
\n" ); document.write( "We observe that (x^2-6x)=x(x-6)
\n" ); document.write( "The denominators are (x-6),x and (x^2-6x)
\n" ); document.write( "and the lcm is x(x-6)
\n" ); document.write( "6x/(x-6) -4/x=24/(x^2-6x)----(1)
\n" ); document.write( "6x/(x-6) -4/x=24/x(x-6)
\n" ); document.write( "Multiplying through out by x(x-6)
\n" ); document.write( "(6x)X(x)-4(x-6)=24
\n" ); document.write( "6x^2-4x+24 = 24
\n" ); document.write( "6x^2-4x=0 (subtracting 24 from both the sides)
\n" ); document.write( "2x(3x-2)=0
\n" ); document.write( "2 cannot be zero
\n" ); document.write( "Therefore either x= 0 or (3x-2) = 0 which gives 3x=2 implying x = 2/3
\n" ); document.write( "x CANNOT be zero as division by zero is not defined
\n" ); document.write( "and the problem has x in two of the denominators
\n" ); document.write( "Answer: Therefore is x = 2/3
\n" ); document.write( "Verification: putting x= 2/3 in
\n" ); document.write( "6x/(x-6) -4/x=24/(x^2-6x) ----(1)
\n" ); document.write( "LHS= [6X(2/3)]/(2/3-6)-4/[(2/3)] =[ 4 divided by (2-18)/6]-6
\n" ); document.write( "=[4 divided by(-16)/3]-6
\n" ); document.write( "=[4X(-3/16)]-6 = (-12/16)-6 = -3/4-6=-27/4
\n" ); document.write( "(cancelling 4 in the nr and in the dr)
\n" ); document.write( "RHS= 24/(x^2-6x)=24/[4/9-4]
\n" ); document.write( "=24/[(-32/9)]=-(24X9)/32=-3X9/4
\n" ); document.write( "(cancelling 8 in the nr and in the dr) = -27/4 =LHS \n" ); document.write( "