Solve for: (4)/(x-2)-(2)/(x+4)

Expression: $\frac{ 4 }{ x-2 }-\frac{ 2 }{ x+4 }$

Write all numerators above the least common denominator $\left( x-2 \right) \times \left( x+4 \right)$

$\frac{ 4\left( x+4 \right)-2\left( x-2 \right) }{ \left( x-2 \right) \times \left( x+4 \right) }$

Distribute $4$ through the parentheses

$\frac{ 4x+16-2\left( x-2 \right) }{ \left( x-2 \right) \times \left( x+4 \right) }$

Distribute $-2$ through the parentheses

$\frac{ 4x+16-2x+4 }{ \left( x-2 \right) \times \left( x+4 \right) }$

Simplify the expression

$\frac{ 4x+16-2x+4 }{ {x}^{2}+4x-2x-8 }$

Collect like terms

$\frac{ 2x+16+4 }{ {x}^{2}+4x-2x-8 }$

Add the numbers

$\frac{ 2x+20 }{ {x}^{2}+4x-2x-8 }$

Collect like terms

$\frac{ 2x+20 }{ {x}^{2}+2x-8 }$