3х+9 2х-13 -------- + ------------- = 2 3х-1 2x+5

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вопрос

To simplify the equation, we need to find a common denominator for the fractions on the left side of the equation.

The common denominator for the two fractions is (3x-1)(2x+5).

Rewrite the equation with the common denominator:

(3x+9)(2x+5)/(3x-1)(2x+5) + (2x-13)(3x-1)/(3x-1)(2x+5) = 2

Now multiply the numerators:

(6x^2 + 15x + 18x + 45 + 6x^2 - 26x - 13) / ((3x-1)(2x+5)) = 2

Combine like terms:

(12x^2 - 3x + 32) / ((3x-1)(2x+5)) = 2

Now set the numerator equal to the denominator:

12x^2 - 3x + 32 = 2*(3x-1)(2x+5)

12x^2 - 3x + 32 = 6x^2 + 15x - 2

Rearrange into standard form:

6x^2 - 18x + 34 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-(-18) ± √((-18)^2 - 4634)) / 2*6
x = (18 ± √(324 - 816)) / 12
x = (18 ± √(-492)) / 12
x = (18 ± 2√(123)i) / 12
x = (9 ± √(123)i) / 6

Therefore, the solution to the equation is x = (9 ± √(123)i) / 6.