We have 3 non-removable restrictions at x = -4, x = 1, and x = -1.
How to see if it is removable or non-removable?
Here we have the expression:
[tex]\frac{x - 3}{x + 4} /\frac{x^2 - 1}{x}[/tex]
This can be rewritten as:
[tex]\frac{x-3}{x + 4} *\frac{x}{x^2 - 1}[/tex]
We can rewrite the denominator of the second fraction as:
[tex]x^2 - 1 = (x - 1)*(x + 1)[/tex]
Then we rewrite the expression as:
[tex]\frac{x-3}{x + 4} *\frac{x}{(x- 1)*(x + 1)} = \frac{x*(x - 3)}{(x + 4)*(x + 1)*(x - 1)}[/tex]
So, none of the factors in the denominator is also in the numerator meaning that none of the restrictions is removable.
Then we have 3 non-removable restrictions at:
x = -4, x = -1, x = 1.
If you want to learn more about rational expressions:
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