What is the simplified form of x plus 1 over x squared plus x minus 6 : x squared plus 5x plus 4 over x plus 4?

1 / (x-2) (x+3)

Step-by-step explanation:

Given in the question the expression:

(x + 1) / (x² + x - 6) : (x² + 5x + 4) / (x+4)

factorisation of (x² + x - 6) = (x-2) (x+3) by using quadratic equation

(x + 1) / (x-2) (x+3) : (x² + 5x + 4) / (x+4)

Taking reciprocal to convert : into *

(x + 1) / (x-2) (x+3) x (x+4) / (x² + 5x + 4)

factorisation of (x² + 5x + 4) = (x+1) (x+4) by using quadratic equation

(x + 1) / (x-2) (x+3) x (x+4) / (x+1) (x+4)

cancel (x + 1) from both expression

1 / (x-2) (x+3) x (x+4) / (x+4)

cancel (x+4)

1 / (x-2) (x+3) Simplified form