Subtract. Simplify by removing a factor of 1 when possible.

(9p^b)/p^2-b^2 - p-b/p+b.

Thank you. These problems, I don't understand at all. I'm sorry.

The way the expression is typed is probably different from the book for lack of parentheses. When it is type-set, parentheses are not required on the numerator and denominator. When interpreted on one single line, they are required, or else a completely different expression results.

Also, I think 9p^b at the beginning should read 9p^2 (just a guess).

Please check what I assume is the correct interpretation.

(9p^2)/(p^2-b^2) - (p-b)/(p+b)
=(9p^2)/((p+b)(p-b)) - (p-b)²/((p+b)(p-b))
=(9p^2-(p-b)²)/((p+b)(p-b))
=(3p+p-b)(3p-(p-b))/((p+b)(p-b))
=(4p-b)(2p+b)/((p+b)(p-b))

No problem at all! I can help you understand this problem.

To subtract the given expression and simplify it, we need to first find the common denominator between the two terms in the expression. The common denominator in this case is (p^2 - b^2), which is a difference of squares.

Let's break down the expression step by step:

(9p^b) / (p^2 - b^2) - (p - b) / (p + b)

Step 1: Simplify the first term:
We do not have any like terms to simplify in the first term, so we leave it as (9p^b) / (p^2 - b^2).

Step 2: Simplify the second term:
To simplify the second term (p - b) / (p + b), we need to find a common denominator with the first term. In this case, the common denominator is (p^2 - b^2), which is the same as the denominator in the first term.

To get the common denominator, we need to factor the difference of squares (p^2 - b^2) = (p - b)(p + b).

So now, the second term becomes ((p - b)(p - b)) / (p + b).

Step 3: Subtract the two terms:
Now that we have the same denominator for both terms [(p - b)(p + b)], we can subtract them.

(9p^b) / (p^2 - b^2) - ((p - b)(p - b)) / (p + b)

To subtract them, we need to find the least common multiple (LCM) of the two terms' denominators, which is (p^2 - b^2)(p + b).

Now, let's find the equivalent fractions with the common denominator:

For the first term, multiply the numerator and denominator by (p + b), so it becomes:
[(9p^b)(p + b)] / [(p^2 - b^2)(p + b)]

For the second term, we don't need to make any changes since it already has the common denominator:
[(p - b)(p - b)] / (p + b)

Step 4: Simplify the expression:
Now that both terms have the same denominator, we can subtract them.

[(9p^b)(p + b) - (p - b)(p - b)] / [(p^2 - b^2)(p + b)]

After expanding and simplifying the numerator, it becomes:
[9p^(b+1) + 9bp^b - (p^2 - 2pb + b^2)] / [(p^2 - b^2)(p + b)]

Further simplifying, we get:
[9p^(b+1) + 9bp^b - p^2 + 2pb - b^2] / [(p^2 - b^2)(p + b)]

This is the final simplified expression after subtracting and simplifying.

I hope this explanation helps you understand the process. Let me know if you have any further questions!