Subtract the rational expressions:
13

9+p2
−
5

9+p2

Simplify if possible.

Question

Subtract the rational expressions:  
13

9+p2
−
5

9+p2

Simplify if possible.

BlackTom AI · Accepted Answer

First, restate the task in my own words to ensure understanding: we need to subtract two rational expressions that share the same denominator, namely 9 + p^2, so we are computing (13) / (9 + p^2) − (5) / (9 + p^2).
Next, observe that since the denominators are identical, subtraction can be performed by subtracting the numerators while keeping the common denominator unchanged: (13 − 5) / (9 + p^2).
Compute the numerator subtraction: 13 − 5 equals 8, which gives 8 / (9 + p^2).
Consider if there is any further simplification. The fraction 8 / (9 + p^2) is already in lowest terms because 8 and (9 + p^2) share no common factors that can cancel for all real p, and (9 + p^2) cannot be factored to reveal a factor of 8.
Also, note the domain aspect: since p^2 is always nonnegative, 9 + p^2 is always at least 9, so the denominator cannot be zero for real p, which means there are no domain restrictions introduced by this subtraction.
In case you’re thinking about alternative representations, you might consider emphasizing the denominator as a single entity (9 + p^2) rather than expanding or rearranging, because there is no common factor to cancel between the numerator (8) and the denominator beyond what’s already present.
If you were to check your work, you could re-express the original problem as a single fraction over the same denominator and verify that the numerator becomes 8, confirming the result matches the simplification (13 − 5) = 8.
Thus, after subtraction and simplification, the expression simplifies to 8 / (9 + p^2).

ALGII141-027 5.4 Practice Problems

Subtract the rational expressions: 13 9+p2 − 5 9+p2 Simplify if possible.

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