Answer:
The correct option is 4.
Step-by-step explanation:
The given expression is,
[tex]\frac{x+4}{x^2+x-12} \cdot \frac{x+4}{x^2+8x+16}[/tex]
Use grouping method to factorize the denominations.
[tex]\frac{x+4}{x^2+4x-3x-12} \cdot \frac{x+4}{x^2+4x+4x+16}[/tex]
[tex]\frac{x+4}{x(x+4)-3(x+4)} \cdot \frac{x+4}{x(x+4)+4(x+4)}[/tex]
[tex]\frac{x+4}{(x+4)(x-3)} \cdot \frac{x+4}{(x+4)(x+4)}[/tex]
Cancel out the common factor (x+4).
[tex]\frac{1}{x-3} \cdot \frac{1}{x+4}[/tex]
[tex]\frac{1}{(x-3)(x+4)}[/tex]
Therefore the correct option is 4.
