How do you solve #1/(x-6) + 1/(x-2)= 6/5 #?

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Answer 1 · 2017-10-07T11:28:14

Solution : # x =7 ,x= 8/3 #

# 1/(x-6) +1/(x-2) = 6/5#. Multiplying by #5(x-6)(x-2)# on both

sides we get #5(x-2)+5(x-6)=6(x-6)(x-2) # or

#5x-10+5x-30=6(x^2-8x+12) #or

#10x-40= 6x^2-48x+72# or

#6x^2-48x+72-10x+40=0 or 6x^2-58x+112 =0 # or

#3x^2-29x+56 =0 or 3x^2-21x -8x+56 =0# or

# 3x(x-7)-8(x-7) =0 or (x-7)(3x-8) =0#

# :. x =7 ,x= 8/3 :.# Solution : # x =7 ,x= 8/3 # [Ans]