Solve \(\frac{4}{x + 1} - \frac{1}{x} = 1\) over the real numbers.
Answer (3)
x + 1 4 − x 1 = 1 x + 1 = 0 an d x = 0 x = − 1 an d x = 0 D = R ∖ { − 1 , 0 }
x ( x + 1 ) 4 x − ( x + 1 ) = 1 x 2 + x 4 x − x − 1 = 1 x 2 + x 3 x − 1 = 1 3 x − 1 = x 2 + x x 2 + x − 3 x + 1 = 0
x 2 − 2 x + 1 = 0 ( x − 1 ) 2 = 0 x − 1 = 0 x = 1
Ok sorry I guessed this one but it was x = 1 4/(1+1) - 1/1 = 1 2 - 1 = 1 And it's right :)
To solve the equation x + 1 4 − x 1 = 1 , we find that the solution is x = 1 . This was determined by transforming the equation and checking that the solution does not violate any restrictions. Hence, the valid solution for this equation is x = 1 .
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