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

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Answer 1 · 2017-09-11T18:21:38

#color(magenta)(x=4#

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

multiply both sides by #x-2#

#:.x-(x-2)/(x-3)=x-2#

multiply both sides by #x-3#

#:.x(x-3)-(x-2)=(x-2)(x-3)#

#:.x^2-3x-x+2=x^2-5x+6#

#:.x^2-x^2-4x+5x=6-2#

#:.color(magenta)(x=4#

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substitute #color(magenta)(x=4#

#:.4/((color(magenta)4)-2)-1/((color(magenta)4)-3)=(1)#

#:.4/2-1/1=1#

#:.2-1=1#

#:.color(magenta)(1=1#