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

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Answer 1 · 2018-06-28T17:31:39

#x=-3, 1/2#

#\frac{2}{x+1}+\frac{5}{x-2}=-2#

#\frac{2}{x+1}+\frac{5}{x-2}+2=0#

#\frac{2(x-2)+5(x+1)+2(x-2)(x+1)}{(x-2)(x+1)}=0#

#\frac{2x-4+5x+5+2x^2-2x-4}{(x-2)(x+1)}=0#

#\frac{2x^2+5x-3}{(x-2)(x+1)}=0#

#\frac{2x^2+6x-x-3}{(x-2)(x+1)}=0#

#\frac{2x(x+3)-(x+3)}{(x-2)(x+1)}=0#

#\frac{(x+3)(2x-1)}{(x-2)(x+1)}=0#

#(x+3)(2x-1)=0\quad (\forall \\ x\ne-1, x\ne2)#

#x+3=0, 2x-1=0#

#x=-3, 1/2#