7х-с/2х-c+2 с+8х/6с+2х

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вопрос

To simplify the expression, we first need to find a common denominator for the fractions:

(7x - c)/(2x - c) + (8x)/(6c + 2x)

Now, to find the common denominator, we need to factor out any common factors between the denominators:

2x - c = (2x - c)
6c + 2x = 2(3c + x)

Therefore, the common denominator is 2(3c + x):

[(7x - c)(2(3c+x))/ (2x - c)(2(3c + x))] + [(8x(2(3c+x)) / (6c + 2x)(2(3c + x))]

Expanding the numerators and denominators, we get:

[14x(3c + x) - c(3c + x) / 2(3c + x)(2x - c)] + [16x(3c + x) / 2(3c + x)(2x - c)]

Simplifying further, we get:

(42cx + 14x^2 - 3c^2 - cx) / [2(3c + x)(2x - c)] + (48cx) / [2(3c + x)(2x - c)]

Now, we can simplify the expression by combining like terms in the numerator:

(41cx + 14x^2 - 3c^2) / [2(3c + x)(2x - c)] + (48cx) / [2(3c + x)(2x - c)]

Therefore, the simplified expression is:

(41cx + 14x^2 - 3c^2 + 48cx) / [2(3c + x)(2x - c)]