X's constant

Algebra Level 2

Simplify

x x ( x + 1 ) x + 1 x x + 1 ( x + 1 ) x + x x − 1 ( x − 1 ) x x x ( x − 1 ) x − 1 \frac {x^x(x+1)^{x+1}} {x^{x+1}(x+1)^x} +\frac {x^{x-1}(x-1)^x} {x^x(x-1)^{x-1}}

Take x ≠ 1 x \ne 1 .

x x x^x ( x + 1 ) x + 1 (x+1)^{x+1} 2 2 x x

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1 solution

Tom Engelsman
Feb 11, 2021

The above expression simplifies into:

x + 1 x + x − 1 x = 1 + 1 x + 1 − 1 x = 2 . \frac{x+1}{x} + \frac{x-1}{x} = 1 + \frac{1}{x} + 1 - \frac{1}{x} = \boxed{2}.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes, it's quite simple as long as one simplifies the fractions before adding.

Richard Desper - 4 months ago

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