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

Mar 20, 2018

The simplified expression is $\sin \frac{x}{\sin x + 2}$.

#### Explanation:

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

$\frac{{\sin}^{2} x - 2 \sin x}{{\sin}^{2} x - 4}$

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:

$\textcolor{w h i t e}{=} \frac{{\sin}^{2} x - 2 \sin x}{{\sin}^{2} x - 4}$

$= \frac{{\left(\sin x\right)}^{2} - 2 \sin x}{{\left(\sin x\right)}^{2} - {2}^{2}}$

$= \frac{\left(\sin x\right) \left(\sin x - 2\right)}{{\left(\sin x\right)}^{2} - {2}^{2}}$

$= \frac{\left(\sin x\right) \left(\sin x - 2\right)}{\left(\sin x + 2\right) \left(\sin x - 2\right)}$

$= \frac{\left(\sin x\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(\sin x - 2\right)}}}}{\left(\sin x + 2\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(\sin x - 2\right)}}}}$

$= \sin \frac{x}{\sin x + 2}$

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.

Mar 20, 2018

$\sin \frac{x}{\sin x + 2}$

#### Explanation:

GCF and difference of squares:
${x}^{2} - x = x \left(x - 1\right)$
$\left({x}^{2} - 4\right) = \left(x + 2\right) \left(x - 2\right)$

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

$\frac{\sin x \cancel{\left(\sin x - 2\right)}}{\left(\sin x + 2\right) \cancel{\left(\sin x - 2\right)}} =$

$\sin \frac{x}{\sin x + 2}$