Question

2x+1/2x-1 - x+1/2x+1 =4/4x^2-1

Answer 1

 

2x  

+  1 x

2

−1 −x  

+  1 x

2

+1 =  

 4 x2

4

−1

      2x+1/2x-1-x+1/2x+1=4/4x2-1    

2x  +  

1

2x

− 1  − x  +  

1

2x

+ 1 =  +  

4

4x2

− 1

Умножим правую и левую часть уравнения на 4x2

8x3 + 2x − 4x2 − 4x3 + 2x + 4x2 =  + 4 − 4x2    

4x3+4x2+4x-4 = 0

Вроде так))))

Answer 2

To solve the given equation, let's follow these steps:

1. Simplify the left side of the equation.
2. Simplify the right side of the equation.
3. Set the simplified left side equal to the simplified right side and solve for x.

Given equation: $\frac{2x + 1}{2x - 1} - \frac{x + 1}{2x + 1} = \frac{4}{4x^2 - 1}$

Step 1: Simplify the left side of the equation. $\frac{2x + 1}{2x - 1} - \frac{x + 1}{2x + 1}$ To combine the fractions, we'll find a common denominator: $\frac{(2x + 1)(2x + 1) - (x + 1)(2x - 1)}{(2x - 1)(2x + 1)}$ $\frac{4x^2 + 4x + 1 - (2x^2 - 1)}{(2x - 1)(2x + 1)}$ $\frac{4x^2 + 4x + 1 - 2x^2 + 1}{4x^2 - 1}$ $\frac{2x^2 + 4x + 2}{4x^2 - 1}$

Step 2: Simplify the right side of the equation. $\frac{4}{4x^2 - 1}$ (already in simplified form)

Step 3: Set the simplified left side equal to the simplified right side and solve for x. $\frac{2x^2 + 4x + 2}{4x^2 - 1} = \frac{4}{4x^2 - 1}$

Now, we'll cross-multiply to eliminate the fractions: $(2x^2 + 4x + 2) \times (4x^2 - 1) = 4 \times (4x^2 - 1)$

Expand both sides: $8x^4 + 16x^3 + 8x^2 - 2x^2 - 4x - 2 = 16x^2 - 4$

Combine like terms: $8x^4 + 16x^3 + 6x^2 - 4x - 2 = 16x^2 - 4$

Rearrange to set it equal to zero: $8x^4 + 16x^3 - 10x^2 - 4x + 2 = 0$

Now, we have a quartic equation. Unfortunately, solving quartic equations algebraically can be quite complex and often involves using numerical methods. If you'd like to proceed with numerical methods or need further assistance, please let me know!