How do you solve #1/x+1/(x-3)=7/(3x-5)#?

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Answer 1 · 2018-03-28T11:34:43

#color(blue)(x=5)#

#color(blue)(x=-3)#

Subtract #7/(3x-5)# from both sides:

#1/x+1/(x-3)-7/(3x-5)=0#

Add LHS:

#((3x-5)(x-3)+x(3x-5)-7x(x-3))/(x(x-3)(3x-5))=0#

Multiply both sides by #x(x-3)(3x-5)#

#(3x-5)(x-3)+x(3x-5)-7x(x-3)=0#

Expand LHS:

#3x^2-14x+15+3x^2-5x-7x^2+21x=0#

Simplify:

#-x^2+2x+15=0#

#x^2-2x-15=0#

Factor:

#(x-5)(x+3)=0=>x=5 and x=-3#