How do you solve #(a+3)/a-6/(5a)=1/a#?

1 Answer
Apr 12, 2017

#color(blue)(a=-4/5#

Explanation:

#(a+3)/a-6/(5a)=1/a#

#:.(a+3)/a-1/a=6/(5a)#

#:.(a+3-1)/a=6/(5a)#

multiply L.H.S and R.H.S by #5a#

#:.(5cancela)^color(green)1/1 xx (a+3-1)/cancela^color(green)1=6/cancel(5a)^color(green)1 xx cancel (5a)^color(green)1/1 #

#:.5(a+3-1)=6#

#:.5(a+2)=6#

#5a+10=6#

#:.5a=6-10#

#:.5a=-4#

#:.color(blue)(a=-4/5#

substitute #color(blue)(a=-4/5#

#:.(-(4/5)+3)/(-4/5)-6/(5(-4/5))=1/(-4/5)#

#:.(-4/5+15/5)/(-4/5)-6/(-20/5)=1 xx -5/4#

#:.(11/5)/(-4/5)-6/-4=-5/4#

#:.11/cancel5^1 xx -cancel5^1/4=-5/4#

#:.11/-4-6/-4=-5/4#

#:.color(blue)(5/-4=5/-4#