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

1 Answer
Sep 7, 2017

Answer:

#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#