Question

How do I simplify? sin²x-sinx2/sin²x-4

Answer 1

The simplified expression is `sinx/(sinx+2)`.

Explanation:

Your input question wasn't really clear, so I'll assume you meant this:

`(sin^2x-2sinx)/(sin^2x-4)`

To solve this question, factor out like terms on the top and bottom like you are solving a quadratic. Then, cancel the ones that are in common with the bottom and the top of the fraction.

Here's what that process looks like:

`color(white)=(sin^2x-2sinx)/(sin^2x-4)`

`=((sinx)^2-2sinx)/((sinx)^2-2^2)`

`=((sinx)(sinx-2))/((sinx)^2-2^2)`

`=((sinx)(sinx-2))/((sinx+2)(sinx-2))`

`=((sinx)color(red)cancelcolor(black)((sinx-2)))/((sinx+2)color(red)cancelcolor(black)((sinx-2)))`

`=sinx/(sinx+2)`

I don't know if this is what you wanted, but this is the answer to the problem I understood. If this isn't what you were asking for, please write a comment letting me know so I can change this.

Answer 2

`sinx/(sinx+2)`

Explanation:

GCF and difference of squares:
`x^2-x= x(x-1)`
`(x^2-4)= (x+2)(x-2)`

Apply them to this:
`(sin²x-2sinx)/(sin²x-4)=`

`(sinxcancel((sinx-2)))/((sinx+2)cancel((sinx-2)))=`

`sinx/(sinx+2)`