157/MR00. problem / Math - Solved Math Problems

MR-157. problem

Solve the following equation:

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

Source: MathReference: Generic Math Textbook - 157.)

Algebra → Quadratic equations, inequalities and systems of equations → Quadratic equations

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

\frac{2 x + 1}{x - 1} + \frac{x - 1}{2 x + 1} - \frac{5 x^{2} + 4}{(x - 1) \cdot (2 x + 1)} = 0

\frac{(2 x + 1) \cdot (2 x + 1) + (x - 1) \cdot (x - 1) - (5 x^{2} + 4)}{(x - 1) \cdot (2 x + 1)} = 0

\frac{{(2 x + 1)}^{2} \cdot {(x - 1)}^{2} - (5 x^{2} + 4)}{(x - 1) \cdot (2 x + 1)} = 0

\frac{4 x^{2} + 4 x + 1 + x^{2} - 2 x + 1 - 5 x^{2} - 4}{(x - 1) \cdot (2 x + 1)} = 0

\frac{2 x - 2}{(x - 1) \cdot (2 x + 1)} = 0

2 x - 2 = 0

2 x = 2

x = \frac{2}{2}

$x = 1$