$\frac{ x-2 }{ 2-\sqrt{ x+2 } } \times \frac{ 2+\sqrt{ x+2 } }{ 2+\sqrt{ x+2 } }$
To multiply the fractions, multiply the numerators and denominators separately$\frac{ \left( x-2 \right) \times \left( 2+\sqrt{ x+2 } \right) }{ \left( 2-\sqrt{ x+2 } \right) \times \left( 2+\sqrt{ x+2 } \right) }$
Use $\left( a-b \right)\left( a+b \right)={a}^{2}-{b}^{2}$ to simplify the product$\frac{ \left( x-2 \right) \times \left( 2+\sqrt{ x+2 } \right) }{ 4-\left( x+2 \right) }$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$\frac{ \left( x-2 \right) \times \left( 2+\sqrt{ x+2 } \right) }{ 4-x-2 }$
Subtract the numbers$\frac{ \left( x-2 \right) \times \left( 2+\sqrt{ x+2 } \right) }{ 2-x }$
Factor out the negative sign from the expression and reorder the terms$\frac{ \left( x-2 \right) \times \left( 2+\sqrt{ x+2 } \right) }{ -\left( x-2 \right) }$
Cancel out the common factor $-\left( x-2 \right)$$-\left( 2+\sqrt{ x+2 } \right)$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$-2-\sqrt{ x+2 }$