Calculate: (x-2)/(2-sqrt(x+2))

Expression: $\frac{ x-2 }{ 2-\sqrt{ x+2 } }$

Multiply the fraction by $\frac{ 2+\sqrt{ x+2 } }{ 2+\sqrt{ x+2 } }$

$\frac{ x-2 }{ 2-\sqrt{ x+2 } } \times \frac{ 2+\sqrt{ x+2 } }{ 2+\sqrt{ x+2 } }$

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

$-2-\sqrt{ x+2 }$