(4х-3)/(3-2х) - (4+5х)/(3+2х) - (3+х-10x^2)/(4x^2-9)

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вопрос

To simplify the expression, we first need to factor each denominator in order to find a common denominator.

Factor the denominators:
Denominator of the first term: (3-2x) = 3 - 2x
Denominator of the second term: (3+2x)
Denominator of the third term: (4x^2 - 9) = (2x - 3)(2x + 3)

Find the common denominator, which is the product of the three denominators:
Common denominator = (3 - 2x)(3 + 2x)(2x - 3)(2x + 3)

Rewrite the fractions with the common denominator:
(4x - 3)(3 + 2x) - (4 + 5x)(2x - 3) - (3 + x - 10x^2)(3 - 2x)

Expand and simplify each term:
(4x - 3)(3 + 2x) = 12x - 8x^2 - 9 - 6x = -8x^2 + 6x - 9
(4 + 5x)(2x - 3) = 8x - 12 + 10x^2 - 15x = 10x^2 - 7x - 12
(3 + x - 10x^2)(3 - 2x) = -9 - 6x + 3 - 2x + 30x^2 - 20x^2 = 8x^2 - 8x - 6

Combine the simplified terms:
(-8x^2 + 6x - 9) - (10x^2 - 7x - 12) - (8x^2 - 8x - 6)
= -8x^2 + 6x - 9 - 10x^2 + 7x + 12 - 8x^2 + 8x + 6
= -8x^2 + 10x^2 - 8x^2 + 6x + 7x + 8x - 9 + 12 + 6
= -6x^2 + 21x + 9

Therefore, the simplified expression is: -6x^2 + 21x + 9.