Question

Помогите пожалуйста! х`2+2х-4/(х'2-16)*2х+9х/(4-х)(х+4) с объяснением

Answer 1

$\frac{x^2+4x-4}{x^2-16}*2x+ \frac{9x}{(4-x)(x+4)}=\\\\ \frac{2x^3+4x^2-8x}{(x-4)(x+4)}+ \frac{9x}{(4-x)(x+4)}=\\\\ \frac{8x^3+16x^2-32x-2x^4-4x^3+8x^2+9x^2-36x}{(x-4)(x+4)(4-x)}=\\\\ \frac{-2x^4+4x^3+33x^2-68x}{(x-4)(x+4)(4-x)}= \frac{x(4-x)(2x^2+4x-17)}{(x-4)(x+4)(4-x)}=\\\\ \frac{x(2x^2+4x-17)}{(x-4)(x+4)}= \frac{2x^3+4x^2-17x}{x^2-16}$

Возможно, существует более оптимальная версия решения

Answer 2

Simplifying the Expression

To simplify the expression 2x + 2x - 4 / (x^2 - 16) * 2x + 9x / (4 - x)(x + 4), we can follow the order of operations (PEMDAS/BODMAS) and simplify each part step by step.

Let's break down the expression and simplify it:

1. Combine like terms: - 2x + 2x = 4x - 2x + 9x = 11x

2. Simplify the fractions: - 4 / (x^2 - 16) To simplify this fraction, we need to factor the denominator, which is a difference of squares. The denominator can be factored as (x - 4)(x + 4). Therefore, the fraction becomes 4 / (x - 4)(x + 4).

- 9x / (4 - x)(x + 4) Similarly, we need to factor the denominator, which is (4 - x)(x + 4).

3. Combine the simplified terms: - 4x + 4 / (x - 4)(x + 4) * 2x + 9x / (4 - x)(x + 4)

4. Multiply the fractions: - 4 / (x - 4)(x + 4) * 2x = (8x) / (x - 4)(x + 4) - 9x / (4 - x)(x + 4) remains the same.

5. Combine the terms again: - (8x) / (x - 4)(x + 4) + 9x / (4 - x)(x + 4)

Final Simplified Expression

The final simplified expression is:

[(8x) / (x - 4)(x + 4)] + [9x / (4 - x)(x + 4)]

Please note that this is a simplified form of the given expression. If you have any further questions or need additional assistance, feel free to ask!