Question 231449
I can get you an answer, but the answer isn't pretty.


It's not pretty because (2x-3) does not divide evenly into (16x^2 - 54x).


The equation is:


2x/2x-3 = ?/8x-27


Multiply both sides of the equation by (8x-27) to get:


? = (2x*(8x-27))/(2x-3)


Simplify the numerator to get:


? = (16x^2 - 54x) / (2x-3)


Divide (2x-3) into (16x^2 - 54x) to get:


? = 8x - 15 - (45/(2x-3))


That's your answer.


Your original equation becomes:


2x / (2x-3) = (8x - 15 - (45/(2x-3))) / (8x-27)


I proved this is correct by working backwards.


It's easier to confirm by using any real value for x and solving.


Let x = 5.


2x / (2x-3) = (8x - 15 - (45/(2x-3))) / (8x-27) becomes:


2*5 / (2*5-3) = (8*5 - 15 - (45/(2*5-3))) / (8*5 - 27).


Simplify to get:


(10 / 7) = (40 - 15 - (45/7)) / (40 - 27)


Combine like terms to get:


(10 / 7) = (18.57142857 / 13)


Simplify further to get:


1.428571429 = 1.428571429


Since the equation is true, then the answer is confirmed.


That answer is:


? = 8x - 15 - (45/(2x-3))