Answer
$7 - z$
Restriction: $z \ne -7$
Work Step by Step
Let's first take a look at the problem to see what we can cancel out from the numerator and denominator:
$\dfrac{49 - z^2}{z + 7}$
We can factor the binomial in the numerator because it is the difference of two squares. The formula for factoring this binomial is as follows:
$a^2 - b^2 = (a + b)(a - b)$
Let's factor the numerator using this formula:
$\dfrac{(7 - z)(7 + z)}{z + 7}$
We can divide the numerator and denominator by $z + 7$:
$7 - z$
To find out if there are any restrictions on the variables, we need to find which values of $z$ will cause the denominator to equal zero, which would make the whole expression undefined. Let's set the denominator equal to zero and solve for $z$:
$z + 7 = 0$
Subtract $7$ from each side of the equation:
$z = -7$
Restriction: $z \ne -7$
