How do you solve #1/(x-1) +2/(x-2) + 3/(x-3) = 6/(x+6)# ?

Question

#1/(x-1) +2/(x-2) + 3/(x-3) = 6/(x+6)#

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Answer 1 · 2018-05-29T13:45:09

#x=12/5,6/5#

#1/(x-1) +2/(x-2) + 3/(x-3) = 6/(x+6)#

Apply common denominator,

#(1(x-2)(x-3)+2(x-1)(x-3)+3(x-1)(x-2))/((x-1)(x-2)(x-3))=6/(x+6)#

Simplify,

#(6x^2-22x+18)/(x^3-6x^2+11x-6)=6/(x+6)#

Cross multiply,

#(6x^2-22x+18)(x+6)=6(x^3-6x^2+11x-6)#

Expand,

#6x^3+14x^2-114x+108=6x^3-36x^2+66x-36#

Move all terms to the left,

#50x^2-180x+144=0#

Divide both sides by #2#,

#25x^2-90x+74=0#

Factor,

#(5x-12)(5x-6)=0#

Solve,

#x=12/5,6/5#