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Solve 4/(x + 1) - 1/x = 1 over the real numbers.

Sagot :

Lilith
[tex]\frac{ 4}{x + 1} - \frac{1}{x} = 1 \\ \\x+1\neq 0 \ \ \ and \ \ \ x\neq 0 \\ \\x\neq -1 \ \ \ and \ \ \ x\neq 0 \\ \\D=R\setminus \left \{ -1,0 \right \}[/tex]

[tex]\frac{ 4x- (x+1)}{x(x + 1)} = 1 \\ \\\frac{ 4x- x-1 }{x^2+ x}=1 \\ \\\frac{ 3x -1 }{x^2 + x} = 1 \\ \\3x-1=x^2+x\\ \\ x^2+x-3x+1=0[/tex]

[tex]x^2-2x+1=0 \\ \\ (x-1)^2=0 \\ \\x-1=0 \\ \\x=1[/tex]
 

Dannymal
Ok sorry I guessed this one but it was x = 1
4/(1+1) - 1/1 = 1
2 - 1 = 1
And it's right :)
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