186k views
4 votes
Find the following sum or dif (4)/(3z+5)+(6z-30)/(25-9ᶻ²)

1 Answer

2 votes

Final answer:

To sum the two given rational expressions, we find a common denominator, which is (25-9z²), and then add the adjusted numerators to get the final simplified expression (-6z - 10) / (25 - 9z²).

Step-by-step explanation:

The student is asking to find the sum of two rational expressions: (4)/(3z+5) and (6z-30)/(25-9z²). To add these, a common denominator must be found. The second denominator factors as (25 - 9z²) = (5-3z)(5+3z). Since 3z+5 is already part of this, the first fraction can be rewritten over this common denominator by multiplying the numerator and denominator by (5-3z). Doing so, we have:

(4)(5-3z)/(25 - 9z²) + (6z-30)/(25-9z²)

The numerators can now be added:

(20 - 12z + 6z - 30) / (25 - 9z²) = (-12z + 6z + 20 - 30) / (25 - 9z²)

Simplifying the numerator yields:

(-6z - 10) / (25 - 9z²)

Which is the simplified form of the given expression.

User Dafmetal
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories