Answer:
Step-by-step explanation:
To add two rational expressions with unlike denominators, you need to first find a common denominator and then add the numerators.
The common denominator for the two given rational expressions is 4x^2 + 25x - 21.
The first expression can be written as (x - 5)/(4x^2 + 25x - 21), and the second expression as (4x^2 + 15x + 9)/(4x^2 + 25x - 21).
To find the numerators for these rational expressions, we multiply each fraction by the common denominator. We get:
x - 5 = (x - 5) * (4x^2 + 25x - 21) / (4x^2 + 25x - 21) = 4x^3 + 20x^2 - 4x - 105
and
4x^2 + 15x + 9 = (4x^2 + 15x + 9) * (4x^2 + 25x - 21) / (4x^2 + 25x - 21) = 4x^3 + 34x^2 + 6x + 189.
Now that we have the numerators, we can add the two rational expressions to get the result:
x - 5/4x^2 - 25x - 21 + 4x^2 + 15x + 9 = 4x^3 + 54x^2 + 2x + 84 / (4x^2 + 25x - 21)