Question

Simplify the expression: Ava simplified the expression and said that the value is -1. Is Ava's solution correct? If not, find and explain her mistake. Give the correct solution.

Answer 1

Ava correctly factored the denominator:

(3y - 2x) = [-(2x - 3y)] 2

But when she took the negative outside the braces, she did not keep the (-1) squared.

The correct solution is 1.

Explanation:

used this and it was correct

Answer 2

Ava's solution was not correct.

The correct solution is 1.

Explanation:

The expression Ava was to simplify(as seen in the attachment) is:

`((2x-3y)^2)/((3y-2x)^2)`

`3y-2x=-2x+3y=-(2x-3y)`

On substitution of the result above into the denominator, we have:

`((2x-3y)^2)/((-(2x-3y))^2)\\=((2x-3y)^2)/((-1)^2(2x-3y)^2)\\\\\text{Canceling out the like term} (2x-3y)^2, \text{we have:}\\=(1)/((-1)^2)\\\\=1`

Therefore:

Ava did not take the square of the negative sign. This led her to have a negative result.

• Ava's solution was not correct.
• The correct solution is 1.