someone please help me understand how this is done.state all the restritions on the variable 7x-13/x^2-16
Your problem:
7x - 13
-------
x^2 - 16
The restrictions are that x cannot equal 4 or -4.
The denominator of a fraction cannot equal 0.
I hope this helps and is what you were asking.
To understand the restrictions on the variable in the expression 7x - 13 / (x^2 - 16), we need to consider the domain of the expression. The domain refers to the values that x can take without causing any undefined or illegal operations.
In this case, we have a fraction with a denominator of (x^2 - 16). For the fraction to be defined, the denominator cannot be zero. Therefore, we need to find the values of x that make the expression (x^2 - 16) equal to zero.
To solve the equation x^2 - 16 = 0, we can factor it:
(x - 4)(x + 4) = 0
This equation is satisfied when either (x - 4) = 0 or (x + 4) = 0. Therefore, the values of x that make the denominator zero are x = 4 and x = -4.
Hence, the restrictions on the variable x in the expression 7x - 13 / (x^2 - 16) are that x cannot equal 4 or -4. These values must be excluded from the domain to ensure the expression is defined.