Question 92406
{{{6/(x+3) - 3/(x+6) = 4/(x+3)}}} Start with the given equation


{{{(x+3)(x+6)(6/(x+3) - 3/(x+6)) =(x+3)(x+6)(4/(x+3))}}} Multiply both sides by the LCD


{{{6(x+6) - 3(x+3) =4(x+6)}}} Distribute and multiply



{{{6x+36-3x-9=4x+24}}} Distribute again





{{{3x+36-9=4x+24}}}  Combine the variable terms 6x and  -3x  on the left side to get 3x




{{{3x+27=4x+24}}}  Combine the constant terms 36 and  -9  on the left side to get 27




{{{3x=4x+24-27}}} Subtract 27 from both sides



{{{3x-4x=24-27}}} Subtract 4x from both sides




{{{-1 x=24-27}}} Combine like terms {{{3 x}}} and {{{-4 x}}} on the left side to get {{{-1 x}}}





{{{-1 x=-3}}} Combine like terms -27 and 24 on the left side to get -3






{{{x=(-3)/(-1)}}} Now divide both sides by  -1 to isolate and solve for x



{{{x= 3}}} Reduce




So our answer is

{{{x= 3}}}



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Check:

{{{6/(x+3) - 3/(x+6) = 4/(x+3)}}} Start with the given equation


{{{6/(3+3) - 3/(3+6) = 4/(3+3)}}} plug in the answer x=3


{{{6/6 - 3/9 = 4/6}}} Add


{{{(3/3)(6/6) - (2/2)(3/9) = 4/6}}} Multiply both fractions by a form of 1 to make both denominators equal


{{{18/18 - 6/18 = 4/6}}} Multiply


{{{12/18 = 4/6}}} Subtract


{{{2/3 = 2/3}}} Reduce both sides. So our answer is verified