Question

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

Answer 1

`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`