How do you solve #\frac{4x + 1}{x - 2} + 2/x = \frac{- 4}{x^{2} - 2x}#?

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Answer 1 · 2016-09-21T10:29:28

#x=-3/4#

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

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

Now as #x(x-2)# is in denominator #x# cannot take values #0# or #2# i.e. these values are out of domain. Multiplying by #x(x-2)# the above becomes

#x(4x+1)+2(x-2)=-4# or

#4x^2+x+2x-4=-4# or

#4x^2+3x=0# or

#x(4x+3)=0#

But as #x!=0#, #4x+3=0# or #4x=-3# or #x=-3/4#