How do you solve #1/2(x-3)+3/(2-x)=5x#?

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Answer 1 · 2015-12-01T03:37:15

#x=0,15/9#

#(x-3)/2+3/(2-x)=5x#

Achieve a common denominator of #2(2-x)#.

#(x-3)/2((2-x)/(2-x))+(3/(2-x))(2/2)=5x#

#((-x^2+2x+3x-6)+6)/(4-2x)=5x#

#-x^2+5x=5x(4-2x)#

#-x^2+5x=-10x^2+20x#

#9x^2-15x=0#

#x(9x-15)=0#

#{(x=0),(9x-15=0rarrx=15/9):}#

Check to make sure that neither answer will cause a denominator to be #0#.