Question

table of contents > module 7: rational expressions and equations > practice: add and subtract rational express practice: add and subtract rational expre part i practice: add and subtract rational expressions part i score: 1/6 answered: 1/6 question 2 subtract, and state the difference in simplest form \\(\frac{z^2}{z - 9} - \frac{81}{z - 9}\\) where \\(z \
eq -9\\) \\(\circ 9\\) \\(\circ z + 9\\) \\(\circ z - 9\\) \\(\circ \frac{z^2 - 81}{z - 9}\\)

Explanation:

Step1: Subtract the numerators

Since the denominators are the same ($z - 9$), we subtract the numerators: $\frac{z^2 - 81}{z - 9}$.

Step2: Factor the numerator

Factor $z^2 - 81$ as a difference of squares: $z^2 - 81=(z + 9)(z - 9)$. So the expression becomes $\frac{(z + 9)(z - 9)}{z - 9}$.

Step3: Cancel common factors

Cancel out the common factor $(z - 9)$ (since $z
eq - 9$, $z - 9
eq0$ when $z
eq9$ but we already have $z
eq - 9$ and the cancellation is valid for $z
eq9$ too). We get $z + 9$.

Answer:

$z + 9$ (corresponding to the option "z + 9")