Simplify the complex fraction.

x plus open parentheses four x over y closed parentheses over seven over three x
A.fifteen x sqaured over seven y
B.seven x open parentheses y plus four closed parentheses over three x y
C.three x squared open parentheses y plus four clsed parentheses over seven y
D.3 open parentheses y plus four closed parentheses over seven y

1 answer

The correct answer is B.

To simplify the complex fraction, we need to multiply both the numerator and the denominator by the reciprocal of the denominator of the complex fraction.

[(x + 4x/y) / 7] / 3x
= [(xy + 4x) / (7y)] / 3x
= (xy + 4x) / (7y * 3x)
= (xy + 4x) / (21xy)
= (7x(y + 4)) / (21xy)
= (7x(y + 4)) / (3 * 7xy)
= (7x(y + 4)) / (3 * 7xy)
= (y + 4) / (3y)
= (7y + 4) / 3y
= 7(y + 4) / 3y
= 7(y + 4) / 3y
= (7y + 28) / 3y
= (7y + 28) / 3y
= 7(y + 4) / 3y

Therefore, the simplified expression is 7(y + 4) / 3y, which is option B.
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