Answer: To simplify the expression, let's find a common denominator and combine the terms:
The common denominator for the fractions is (2x^2 + 5x)(2x + 5).
Express each fraction with the common denominator:
3/x = (3 * 2x + 3 * 5) / (x * (2x + 5))
= (6x + 15) / (x * (2x + 5))
-15/ (2x^2 + 5x) = (-15) / ((2x^2 + 5x) * (2x + 5))
2/(2x + 5) = (2 * x) / ((2x + 5) * x)
= 2x / (2x^2 + 5x)
Now, the simplified expression becomes:
(6x + 15) / (x * (2x + 5)) - (15) / ((2x^2 + 5x) * (2x + 5)) + 2x / (2x^2 + 5x)
To combine the fractions, find a common denominator for all terms, which is (x * (2x + 5)) * ((2x^2 + 5x) * (2x + 5)).
Express each fraction with the common denominator:
[(6x + 15) * ((2x^2 + 5x) * (2x + 5)) - 15 * (x * (2x + 5)) + 2x * (x * (2x + 5))] / (x * (2x + 5)) * ((2x^2 + 5x) * (2x + 5))
Simplify the numerator:
(6x + 15) * (2x^3 + 5x^2 + 10x + 25) - 15 * (2x^2 + 5x) + 2x * (2x^2 + 5x)
Expand and simplify:
(12x^4 + 30x^3 + 60x^2 + 150x + 30x^3 + 75x^2 + 150x + 375) - (30x^2 + 75x) + 4x^3 + 10x^2
Combine like terms:
12x^4 + 34x^3 + 85x^2 + 285x + 375 - 30x^2 - 75x + 4x^3 + 10x^2
Simplify further:
12x^4 + 34x^3 - 25x^2 + 210x + 375
So, the simplified expression is 12x^4 + 34x^3 - 25x^2 + 210x + 375.