Question

How do you solve `(12x-5) / (6x+3) = 2 - 5/x`?

Answer 1

`x=-15/19`

Explanation:

NOTE: There's more than one way to skin a cat.

`(12x-5)/(6x+3)=2-5/x`

Step 1: multilply both sides by `x`

`x*((12x-5)/(6x+3))=(2-5/x)*x`

`(12x^2-5x)/(6x+3)=2x-5`

Step 2: multiply both sides by `(6x+3)`

`6x+3*((12x^2-5x)/(6x+3))=(2x-5)*(6x+3)`

`12x^2-5x=12x^2+6x-30x-15`

Step 3: simplify

`-5x=-24x-15`

`19x=-15`

`x=-15/19`

Step 4: check your answer for `x`

`(12x-5)/(6x+3)=2-5/x`

`(12*(-15/19)-5)/(6*(-15/19)+3)=2-5/(-15/19)`

`((-180/19)-(95/19))/((-90/19)+(57/19))=2+5*(19/15)`

`(-180-95)/(-90+57)=2+19/3`

`(-180-95)/(-90+57)=6/3+19/3`

`275/33=25/3`

`11` goes into `275` `25` times and `11` goes into `33` `3` times

`25/3=25/3`