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

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Answer 1 · 2016-06-20T16:53:12

#x=(-3+-sqrt17)/2#

first the denominator shouldn't be 0
so #x!=-1 and -2#
#1/(x+1)-1/(x+2)=1/4#

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

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

#x^2+3x=2#

#x^2+3x+9/4=2+9/4#

#(x+3/2)^2=17/4#

#x+3/2=+-sqrt17/2#

#x=(-3+-sqrt17)/2#