Answer:
HOPES THIS HELPS YA OUT!!!
Explanation:
To solve the given equation:
1/x + a + 1/(x + 2a) + 1/(x + 3a) = 3/x
We can follow these steps:
1. Start by finding a common denominator for all the fractions. The common denominator in this case is (x)(x + 2a)(x + 3a).
2. Multiply each term in the equation by the common denominator to eliminate the fractions.
(x)(x + 2a)(x + 3a)(1/x) + (x)(x + 2a)(x + 3a)(a) + (x)(x + 2a)(x + 3a)(1/(x + 2a)) + (x)(x + 2a)(x + 3a)(1/(x + 3a)) = (x)(x + 2a)(x + 3a)(3/x)
3. Simplify the equation by canceling out terms and distributing the common denominator.
(x + 2a)(x + 3a) + (x)(x + 3a)(x + 2a)(a) + (x)(x + 2a) + (x)(x + 2a)(x + 3a) = 3(x + 2a)(x + 3a)
4. Expand and combine like terms on both sides of the equation.
(x^2 + 5ax + 6a^2) + (x^3 + 5ax^2 + 6a^2x + 2ax^2 + 10a^2x + 12a^3) + (x^2 + 2ax) + (x^3 + 3ax^2 + 2ax^2 + 6a^2x) = 3(x^2 + 5ax + 6a^2)
Simplifying further, we have:
x^2 + 5ax + 6a^2 + x^3 + 5ax^2 + 6a^2x + 2ax^2 + 10a^2x + 12a^3 + x^2 + 2ax + x^3 + 3ax^2 + 2ax^2 + 6a^2x = 3x^2 + 15ax + 18a^2
5. Combine like terms and simplify the equation further.
2x^3 + 9x^2 + 39ax + 24a^2 + 12a^3 = 3x^2 + 15ax + 18a^2
Rearranging the equation, we get:
2x^3 + 9x^2 + 39ax + 24a^2 + 12a^3 - 3x^2 - 15ax - 18a^2 = 0
Simplifying further, we have:
2x^3 + 6x^2 + 24ax + 6a^3 = 0
And this is the simplified form of the equation.