what are the restrictions on this rational expression

Question

y=6/4x+24

 

Answer 1

y=6/(4x) + 24

The restriction is that the denominator can not be equal to zero.

So in this problem, since 4x is in the denominator it can not equal zero.

Find all values of x that give you a zero in the denominator.

4x=0

x=0

So, x=0 is the only restriction for this expression

Answer 2

To find the restrictions on a rational function, find the values of the variable that make the denominator equal 0.

I am not sure whether you have the equation y = 6/(4x) + 24 or y = 6/(4x + 24), so I will demonstrate how to solve each of them.

y = 6/(4x) + 24                       Given equation

4x ≠ 0                                   State that the denominator cannot equal 0

4x/4 ≠ 0/4                             Divide each side by 4

x ≠ 0                                     Simplify each side

or

y = 6/(4x + 24)                     Given

4x + 24 ≠ 0                          State that the denominator cannot equal 0

4x + 24 - 24 ≠ 0 - 24            Subtract 24 from each side

4x ≠ -24                             Simplify

4x/4 ≠ -24/4                       Divide each side by 4

x ≠ -6                                 Simplify