Explanation:
To solve the question, we will have to get the factor of the terms given
Let us follow the steps below
Step 1: Write out the given expression
[tex]\frac{4-x}{x^2+5x-6}\div\frac{x^2-11x+28}{x^2+7x+6}[/tex]
Step 2: simplify each term by writing them in factor form
[tex]\frac{4-x}{(x-1)(x+6)}\div\frac{(x-4)(x-7)}{(x+1)(x+6)}[/tex]
Step 3: Re-write the expression
[tex]\frac{4-x}{(x-1)(x+6)}\times\frac{(x+1)(x+6)}{(x-4)(x-7)}[/tex]
Step 4: Simplify further and cancel out like terms
[tex]\frac{4-x}{x-1}\times\frac{x+1}{(x-4)(x-7)}[/tex]
Step 5: simplify by factoring out the negative sign
[tex]\frac{-(x-4)}{x-1}\times\frac{x+1}{(x-4)(x-7)}[/tex]
Step 6: Resolve the expression
[tex]\frac{-1(x+1)}{(x-1)(x-7)}[/tex]
Thus, we have the simplified form to be
[tex]\frac{-x-1}{(x-1)(x-7)}[/tex]
Then for the restrictions, these will be values of x which makes it undefined
These values are
[tex]x=1\text{ and x=7}[/tex]
