Evaluate: (x^2-36)/(x^2-4x-12) * (x+2)/(9x)

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Expression: $\frac{ {x}^{2}-36 }{ {x}^{2}-4x-12 } \times \frac{ x+2 }{ 9x }$

Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression

$\frac{ \left( x-6 \right) \times \left( x+6 \right) }{ {x}^{2}-4x-12 } \times \frac{ x+2 }{ 9x }$

Write $-4x$ as a difference

$\frac{ \left( x-6 \right) \times \left( x+6 \right) }{ {x}^{2}+2x-6x-12 } \times \frac{ x+2 }{ 9x }$

Factor out $x$ from the expression

$\frac{ \left( x-6 \right) \times \left( x+6 \right) }{ x \times \left( x+2 \right)-6x-12 } \times \frac{ x+2 }{ 9x }$

Factor out $-6$ from the expression

$\frac{ \left( x-6 \right) \times \left( x+6 \right) }{ x \times \left( x+2 \right)-6\left( x+2 \right) } \times \frac{ x+2 }{ 9x }$

Factor out $x+2$ from the expression

$\frac{ \left( x-6 \right) \times \left( x+6 \right) }{ \left( x+2 \right) \times \left( x-6 \right) } \times \frac{ x+2 }{ 9x }$

Cancel out the common factor $x-6$

$\frac{ x+6 }{ x+2 } \times \frac{ x+2 }{ 9x }$

Cancel out the common factor $x+2$

$\left( x+6 \right) \times \frac{ 1 }{ 9x }$

Calculate the product

$\frac{ x+6 }{ 9x }$

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