How do you solve #2/(x-1) - 2/3 =4/(x+1)#?

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Answer 1 · 2016-04-17T23:39:41

#x_1=2# and #x_2=-5#

Start with Least Common Denominator

LCD#=3(x-1)(x+1)# and dividing both sides of the equation by 2.

#2/(x-1)-2/3=4/(x+1)#

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

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

Multiply both sides of the equation by the LCD then simplify

#3(x-1)(x+1)[1/(x-1)-1/3]=3(x-1)(x+1)*[2/(x+1)]#

#[3(x+1)-(x-1)(x+1)]=6(x-1)#

#3x+3-x^2+1=6x-6#

#x^2+3x-10=0#

Solve the quadratic by factoring method

#x^2+3x-10=0#

#(x-2)(x+5)=0#

#(x-2)=0# and #(x+5)=0#

#x_1=2# and #x_2=-5#

God bless....I hope the explanation is useful.