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Question 231449: 2x/2x-3 = ?/8x-27 Could someone please help me find the missing numerator?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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))
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