Question

3 x / (2 x + 1) + 5 x - 1 / (2 x - 1) ​

Answer 1

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Answer 2

It looks like you've provided a mathematical expression:

$\frac{3x}{2x + 1} + 5x - \frac{1}{2x - 1}$

To simplify this expression, we can start by finding a common denominator for the fractions in the expression. The common denominator for $2x + 1$ and $2x - 1$ is $(2x + 1)(2x - 1)$. Let's work through the simplification step by step:

1. Simplify the fractions:
   $\frac{3x}{2x + 1} - \frac{1}{2x - 1} = \frac{3x(2x - 1)}{(2x + 1)(2x - 1)} - \frac{1(2x + 1)}{(2x + 1)(2x - 1)}$ $= \frac{6x^2 - 3x - 2x - 1}{(2x + 1)(2x - 1)} = \frac{6x^2 - 5x - 1}{(2x + 1)(2x - 1)}$

2. Combine the terms:
   $\frac{6x^2 - 5x - 1}{(2x + 1)(2x - 1)} + 5x = \frac{6x^2 - 5x - 1 + 5x(2x + 1)(2x - 1)}{(2x + 1)(2x - 1)}$ $= \frac{6x^2 - 5x + 10x^3 - 10x^2 + 5x}{(2x + 1)(2x - 1)} = \frac{10x^3 - 4x^2}{(2x + 1)(2x - 1)}$

So, the simplified expression is: $\frac{10x^3 - 4x^2}{(2x + 1)(2x - 1)}$