How do you simplify #(x+1)/(x-1)=2/(2x-1)+2/(x-1)#?

2 Answers
Harish Chandra Rajpoot
Jun 26, 2018

#x=3/2#

Explanation:

Given that

#\frac{x+1}{x-1}=\frac{2}{2x-1}+\frac{2}{x-1}#

#\frac{x+1}{x-1}-\frac{2}{2x-1}-\frac{2}{x-1}=0#

#\frac{(x+1)(2x-1)-2(x-1)-2(2x-1)}{(x-1)(2x-1)}=0#

#\frac{2x^2-5x+3}{(x-1)(2x-1)}=0#

#\frac{2x^2-2x-3x+3}{(x-1)(2x-1)}=0#

#\frac{2x(x-1)-3(x-1)}{(x-1)(2x-1)}=0#

#\frac{(2x-3)(x-1)}{(x-1)(2x-1)}=0#

#\frac{2x-3}{2x-1}=0#

#2x-3=0\quad \forall \ x\ne1/2#

#x=3/2#

IZUkuABA
Jun 26, 2018

#x=3/2 or 1.5#

Explanation:

we have
#(x+1)/(x-1)=(2/(2x-1))+(2/(x-1))#
shifting #(2/(x-1))# to other side
#=>(x+1)/(x-1)-(2/(x-1))=(2/(2x-1))#
#=>(x+1-2)/(x-1)=(2/(2x-1))#
#=>cancel(x-1)/cancel(x-1)=(2/(2x-1))#
#=>2x-1=2; =>x=3/2 or 1.5#

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