Question

(2x+1/x-3 +2x-1/x+3)*x²-9/10x²+15

Answer 1

Ответ:

$(2x + \frac{1}{x} - 2x - \frac{1}{x} + 3) \times {x}^{2} - \frac{9}{10} {x}^{2} + 15$

$4x \times {x}^{2} - \frac{9}{10} {x}^{2} + 15$

$4 {x}^{3} - \frac{9}{10} {x}^{2} + 15$

Answer 2

To simplify the expression $(2x+\frac{1}{x-3} + 2x-\frac{1}{x+3}) \cdot \frac{x^2-9}{10x^2+15}$, you can follow these steps:

1. Factor the numerator and denominator of the fraction $\frac{x^2-9}{10x^2+15}$:

   $\frac{x^2-9}{10x^2+15} = \frac{(x+3)(x-3)}{5(2x^2+3)}$

2. Rewrite the original expression with the factored fraction:

   $(2x+\frac{1}{x-3} + 2x-\frac{1}{x+3}) \cdot \frac{(x+3)(x-3)}{5(2x^2+3)}$

3. Combine like terms in the first part of the expression:

   $(4x+\frac{1}{x-3} - \frac{1}{x+3}) \cdot \frac{(x+3)(x-3)}{5(2x^2+3)}$

4. Now, you can simplify further by canceling out common factors between the numerators and denominators:

   $4x(x+3)(x-3) + \frac{(x+3)(x-3)}{5(x+3)(x-3)} - \frac{(x+3)(x-3)}{5(x+3)(x-3)}$

5. The terms $\frac{(x+3)(x-3)}{5(x+3)(x-3)}$ cancel out because they have the same numerator and denominator.

6. Simplify further:

   $4x(x+3)(x-3)$

So, the simplified expression is $4x(x+3)(x-3)$.