Question

Simplify the complex fraction:
x+(4x/y)/(7/3x)

I know that the answer is 3x^2(y+4)/7y. I don't know how to get this answer. Can someone please help me walk through this and figure out how to simplify it? I would be so grateful.

Answer 1

x+(4x/y)/(7/(3x)) = x + (4x/y)(3x/7) = x + (12x^2)/(7y)
From here there is no way to get the alleged answer.
I suspect a typo in either the question or the answer.

Answer 2

Okay it's a complex fraction, so it's (x+(4x/y)) / (7/3x). I'm not sure how else I would type this.

Answer 3

Aha! The parens make a big difference!

(x+(4x/y)) / (7/3x)
= (xy+4x)/y * 3x/7
= (7(xy+4x) + 3x^2)/(7y)
= (7xy+28x+3x^2)/(7y)
Still no way to get to 3x^2(y+4)/7y
Hmmm.
(3x^2(y+4)/7y)*(7/(3x)) = xy(y+4)
so, xy(y+4)/(7/3x) = 3x^2(y+4)/7y
Still not sure how to get from xy(y+4) to (x + 4x/y)