Simplify each expression and state any non-permissible values. (4 marks - show your work)

4x-1 divided by x^2+7x+12 divided by 2x-1 divided by x^2 +x- 12 is the expression

Help me please and thank you.

(4x-1)/[(x+3)(x+4)] * (x+4)(x-3)/(2x-1)

the (x+4) cancels, not much else to do

To simplify the given expression (4x - 1) / (x^2 + 7x + 12) / (2x - 1) / (x^2 + x - 12), we need to simplify each part and then divide them accordingly.

Step 1: Factorize the denominators of both fractions:

x^2 + 7x + 12 can be factored as (x + 3) * (x + 4)
x^2 + x - 12 can be factored as (x - 3) * (x + 4)

Step 2: Rewrite the expression with the factored denominators:

(4x - 1) / [(x + 3) * (x + 4)] / (2x - 1) / [(x - 3) * (x + 4)]

Step 3: Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator:

[ (4x - 1) / (x + 3) * (x + 4) ] * [ (x - 3) * (x + 4) / (2x - 1) ]

Step 4: Simplify the numerators and denominators:

Numerator:
(4x - 1)(x - 3)(x + 4)

Denominator:
(x + 3)(x + 4)(2x - 1)

Step 5: Cancel out any common factors between the numerator and denominator:

The expression cannot be further simplified.

Non-permissible values are the values of x that make the denominator zero, as division by zero is undefined. By analyzing the factors in the denominator, we find that x = -3, -4, and 1/2 are the non-permissible values, as they would result in division by zero.