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

Answer:

Ava's solution was not correct.

The correct solution is 1.

Step-by-step explanation:

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

$\dfrac{(2x-3y)^2}{(3y-2x)^2}$

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

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

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

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.