Answer:
Option B is correct.
Step-by-step explanation:
We have given an expression:
[tex]\frac{\frac{(x+1)}{x^2+x-6}}{\frac{x^2+5x+4}{(x+4)}}[/tex]
After rearranging the terms from [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]
We will get [tex]\frac{(x+1)(x+4)}{(x^2+x-6)(x^2+5x+4)}[/tex]
Now, we will simplify the terms
[tex]\frac{(x+4)(x+1)}{(x^2+3x-2x-6)(x^2+4x+x+4)}[/tex]
After further simplification we will get
[tex]\frac{(x+4)(x+1)}{(x(x+3)-2(x+3))(x(x+4)+1(x+4))}[/tex]
Now, we will get
[tex]\frac{(x+4)(x+1)}{(x-2)(x+3)(x+1)(x+4)}[/tex]
Now, cancel out the common terms from numerator and denominator which is (x+4)(x+1) we will get
[tex]\frac{1}{(x-2)(x+3)}[/tex]
Therefore, Option B is correct.
