Rational Expressions

Question

I'm having trouble figuring out the answer to this question so could somebody explain it to me and give me the answer as well? It would really help! Is the answer A, B, C, or D? If you respond, thank you for your help! This is for Grade 11 functions, or as I think they call it in america, algebra 1.

(x+1) divided by 2(x-1)(4x+1)

Is the answer:

A. one restriction on x.

B. two restrictions on x.

C. three restrictions on x.

D. four restrictions on x.

Answer 1

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

In math, division by zero is undefined. So if the denominator of a rational expression equals zero, the value of the expression is undefined. So the values of x that make the denominator equal to zero are restricted (excluded from the domain of the function). In your case if either (x-1) = 0 or (4x+1) = 0, the function is undefined. So x cannot equal 1 or -1/4. Sounds like two restrictions to me.