SOLUTION: 6x/x-6 -4/x=24/x^2-6x show me step by step how to solve

Question 29188: 6x/x-6 -4/x=24/x^2-6x
show me step by step how to solve
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
If the given problem is 6x/(x-6) -4/x=24/(x^2-6x) ----(1)
We observe that (x^2-6x)=x(x-6)
The denominators are (x-6),x and (x^2-6x)
and the lcm is x(x-6)
6x/(x-6) -4/x=24/(x^2-6x)----(1)
6x/(x-6) -4/x=24/x(x-6)
Multiplying through out by x(x-6)
(6x)X(x)-4(x-6)=24
6x^2-4x+24 = 24
6x^2-4x=0 (subtracting 24 from both the sides)
2x(3x-2)=0
2 cannot be zero
Therefore either x= 0 or (3x-2) = 0 which gives 3x=2 implying x = 2/3
x CANNOT be zero as division by zero is not defined
and the problem has x in two of the denominators
Answer: Therefore is x = 2/3
Verification: putting x= 2/3 in
6x/(x-6) -4/x=24/(x^2-6x) ----(1)
LHS= [6X(2/3)]/(2/3-6)-4/[(2/3)] =[ 4 divided by (2-18)/6]-6
=[4 divided by(-16)/3]-6
=[4X(-3/16)]-6 = (-12/16)-6 = -3/4-6=-27/4
(cancelling 4 in the nr and in the dr)
RHS= 24/(x^2-6x)=24/[4/9-4]
=24/[(-32/9)]=-(24X9)/32=-3X9/4
(cancelling 8 in the nr and in the dr) = -27/4 =LHS
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