Question

Simplify the sum. State any restrictions on the variable.
(7y+9)/(y-9) + (8y+5)/(y-9)
Select the correct choice below and dill in the answer box(es) to complete your choice.
1)(7y+9)/(y-9) +(8y+5)/(y-9)=____ for y(=/) (Simplify your answers. Usw a comma to separate answers as needed.)
2)(7y+9)/(y-9) +(8y+5)/(y-9)=____ for all values of y. (Simplify your answer.)

Answer 1

To simplify the sum \(\frac{7y+9}{y-9} + \frac{8y+5}{y-9}\), we can combine the fractions since they have a common denominator:

\[
\frac{7y+9 + 8y+5}{y-9} = \frac{(7y + 8y) + (9 + 5)}{y-9}
\]

Combine the like terms in the numerator:

\[
7y + 8y = 15y
\]
\[
9 + 5 = 14
\]

So, we get:

\[
\frac{15y + 14}{y - 9}
\]

Now let's state any restrictions on the variable \(y\). The denominator \(y - 9\) cannot be zero. Therefore, we have:

\[
y - 9 \neq 0 \implies y \neq 9
\]

This means we cannot allow \(y\) to equal 9.

The final answers are:

1) \(\frac{15y + 14}{y - 9}\) for \(y \neq 9\).

2) \(\frac{15y + 14}{y - 9}\) for all values of \(y\), assuming \(y \neq 9\).

Thus, it simplifies to:

1) **\(\frac{15y + 14}{y - 9}\) for \(y \neq 9\)**.
2) **\(\frac{15y + 14}{y - 9}\) for all values of \(y\) with the restriction \(y \neq 9\)**.