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

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Answer 1 · 2017-03-31T09:05:43

#x = -5 or 2#

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

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

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

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

#implies# #(6-2x)3 = 2(x^2-1)#
#implies# #(3-x)3=x^2-1#
#implies##x^2+3x-10=0#

[ solution of a general quadratic equation of the form #ax^2+bx+c=0# is given by
#x=(-b+-sqrt(b^2-4ac))/(2a)#]

#implies# #x= (-3+-sqrt(9+40))/2#
#implies##x = (-3+-7)/2#
#implies##x = -5, 2#