Question

Which expression is equivalent to the following complex tion:

[{24}{y} div {3y + 5x}{2(y - 2x)}]

a) ({3y - 5x}{2(y - 2x)})
b) (xy)
c) (2(y - 2x) div (3 - 6x))
d) (2(y - 2x))

Answer 1

The expression [{24}{y} div {3y + 5x}{2(y - 2x)}] simplifies to (2y) × [1/(3y + 5x)], which is not equivalent to any of the provided options. The correct answer would be none of the given options.

Step-by-step explanation:

The student is trying to find an expression equivalent to the complex fraction ​​[{24}{y} div {3y + 5x}{2(y - 2x)}].

To simplify this expression, we first rewrite the division as multiplication by the reciprocal.

The expression becomes (24y) × ¼[2(y - 2x)/(3y + 5x)].

Simplifying further, we can cancel out a factor of 12 from the numerator and denominator, which leaves us with (2y) × [1/(3y + 5x)].

If we assume the expression was transcribed correctly, none of the given options (a) ({3y - 5x}/{2(y - 2x)}), (b) (xy), (c) (2(y - 2x) div (3 - 6x)), or (d) (2(y - 2x)) are equivalent to the given fraction.

Therefore, the correct answer would be none of the given options.