How do you solve #\frac { 5} { x } = \frac { 3} { x - 12} + 1#?

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Answer 1 · 2017-10-13T00:40:03

#x_1=7+sqrt(11)*i# and #x_2=7-sqrt(11)*i#

#5/x=3/(x-12)+1#

#5/x=(x-9)/(x-12)#

#x*(x-9)=5*(x-12)#

#x^2-9x=5x-60#

#x^2-14x+60=0#

Delta: #(-14)^2-4*1*60=-44<0#

Hence #x_1=7+sqrt(11)*i# and #x_2=7-sqrt(11)*i#