Add the rational expressions:
7

2y+9
+
2

2y+9

Simplify if possible.

Question

Add the rational expressions:  
7

2y+9
+
2

2y+9

Simplify if possible.

BlackTom AI · Accepted Answer

We start by identifying that both fractions share the same denominator, which is 2y+9.

Optionally, I can treat the addition as combining over a common denominator: since the denominators are identical, we simply add the numerators while keeping the same denominator.

So we rewrite the sum as (7)/(2y+9) + (2)/(2y+9).

Because the denominators match, the sum of the fractions is ((7) + (2)) / (2y+9).

Compute the numerator addition: 7 + 2 = 9, giving 9/(2y+9).

Next, check for any simplification by canceling common factors between the numerator and the denominator. The numerator is 9, whose factors are 1, 3, 9, and the denominator is 2y+9, which depends on y. There is no constant factor in common unless y adopts a specific value that makes 2y+9 share a factor with 9; in general, there is no common factor to cancel, so the expression is already in simplest form.

Additionally, note the domain restriction: the original denominators cannot be zero, so 2y+9 ≠ 0, i.e., y ≠ -9/2. This ensures the expression is defined for all allowed y values.

In summary, combining the fractions with a common denominator leads to a numerator total of 9 over the shared denominator, with the usual caveat about the domain where 2y+9 ≠ 0.

ALGII141-027 5.4 Practice Problems

Add the rational expressions: 7 2y+9 + 2 2y+9 Simplify if possible.

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