I am to simplify this expression (2x-3y)^2 / (3y-2x)^2. My answer I keep getting is -1 my teacher states that is not correct. What am I doing wrong?

Question

I am to simplify this expression (2x-3y)^2 / (3y-2x)^2.  My answer I keep getting is -1 my teacher states that is not correct.  What am I doing wrong?

fairygirl0404 · Answer

(2x-3y)^2 / (3y-2x)^2
=(2x-3y)^2 / [-(2x-3y)]^2
=(2x-3y)^2 / (2x-3y)^2
=-1
This is my work.  What am I doing wrong?

caiti2024 · Answer

2x-3y=6 (2x3=6). You multiply the equations to make the x variable equal. The first one becomes 3x*2=6x, and the second becomes 2x*3=6x Then, you can subtract and eliminate them. Please note that the equations do not change if you multiply them by a number, because you can always divide them and again get back your original equation.

fairygirl0404 · Answer

But you have to reduce the expression by cancelling the common factors right.  Somewhere I am making a mistake by getting -1.  It is supposed to be 1.  I am trying to figure were I am making the mistake. @caiti2024

caiti2024 · Answer

The question "3x-2y" is two, and the question 2x-3y is also two. It is simple.  Multiply both sides of the equation by two. Then, distribute and multiply. Then, you equations together. You can do this by simply adding the two left sides and the two right sides separately like this: 


(3x-2y)+(-4x+2y)=(2)+(-4). You group them like terms, then you combine like terms, (-x+0y=-2) and then you simplify to two.

caiti2024 · Answer

This is exactly like the subject in mathematics I am studying currently, and it is also in my classes for the week. All of the steps included are the steps essential to finding the answer. Using coordinate planes also help with understanding expressions and variables like this.

directrix · Answer

@fairygirl0404 

There are two factors of -1 after you rewrite the numerator. -1*-1 = 1

See attachment.