How do you solve #\frac { 9x + 1} { x - 3} = \frac { 18x + 5} { 2x - 5}#?

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Answer 1 · 2017-05-15T04:34:48

#x=-5/3#

We have #(9x+1)/(x-3)=(18x+5)/(2x-5)#

Multiplying both sides by #(x-3)(2x-5)#, we get

#(9x+1)(2x-5)=(18x+5)(x-3)#

or #18x^2-45x+2x-5=18x^2-54x+5x-15#

or #cancel(18x^2)-45x+2x-5=cancel(18x^2)-54x+5x-15#

or #54x-45x+2x-5x=-15+10#

or #6x=-10#

and #x=-10/6=-5/3#

Check - #(9(-5/3)+1)/(-5/3-3)=(18(-5/3)+5)/(2(-5/3)-5)#

i.e. #(-15+1)/(-14/3)=(-30+5)/(-25/3)#

i.e. #(-14)xx(-3/14)=(-25)(-3/25)#

i.e. #3=3#