Given xx+1+x+1x=52 x^2+(x+1)^2x(x+1)=52 4 x^2+4x+2=5 x^2+5 x x^2+x 2=0 x^2+2x x 2=0 x(x+2) (x+2)=0 x=1, 2 ...

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Reducing Equations to Simpler Form

Solve: xx+1+...

Question

Solve:
$\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{5}{2}$

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Solution

Given $\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{5}{2}$
$⟹ \frac{x^{2} + (x + 1)^{2}}{x (x + 1)} = \frac{5}{2}$
$⟹ 4 x^{2} + 4 x + 2 = 5 x^{2} + 5 x$
$⟹ x^{2} + x - 2 = 0$
$⟹ x^{2} + 2 x - x - 2 = 0 ⟹ x (x + 2) - (x + 2) = 0 ⟹ x = 1, - 2$

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