How do you solve #\frac { x + 1} { x - 1} + \frac { 2} { x } = \frac { x } { x + 1}#?

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Answer 1 · 2017-07-21T18:00:00

#x=-1/10pmsqrt10/5#

First our restrictions :

#x!=0andx!=1andx!=-1#

#(x+1)/(x-1)+2/x=x/(x+1) iff #

#(x+1)/(x-1)+2/x-x/(x+1)=0iff#

#((x+1)(x+1)x+2(x-1)(x+1)-x(x-1)x)/((x+1)(x-1)x)=0iff#

#(x+1)(x+1)x+2(x-1)(x+1)-x(x-1)x=0iff#

#(x+1)^2x+2(x^2-1)-x^2(x-1)=0iff#

#(x^2+2x+1)x+2x^2-2-x^3+x^2=0 iff#

#x^3+2x^2+x+2x^2-2-x^3+x^2=0iff#

#5x^2+x-2=0 iff#

#x=(-1pmsqrt(40))/10=-1/10pm2/10sqrt10=-1/10pmsqrt10/5#