How do you multiply #((r+5)/(r^2-2r)) - 1= 1/(r^2-2r)#?

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Answer 1 · 2015-05-21T03:12:45

#((r+5)/(r^2-2r)) - 1= 1/(r^2-2r)#

#((r+5)/(r^2-2r)) - 1 xx ((r^2-2r)/(r^2-2r))= 1/(r^2-2r)#

#((r+5)/(r^2-2r)) - ((r^2-2r)/(r^2-2r))= 1/(r^2-2r)#

#((r+5 - r^2+2r)/cancel(r^2-2r))= 1/cancel(r^2-2r)#

#(r+5 - r^2+2r)= 1#
#- r^2+ 3r +4= 0#

#r^2 - 3r -4= 0#
Factorising by splitting the middle term:

#r^2 - 4r +r -4= 0#
#r(r - 4) +1(r -4)= 0#
#(r+1)(r - 4) = 0#

#color(green)(r = -1,4# are the two solutions