What is x+1<= 1/((x-1)) ?

The solution to x+1<= 1/((x-1)) is x<=-sqrt(2)\lor 1<x<= sqrt(2)

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x+1<= 1/((x-1))

x + 1 \leq \frac{1}{( x - 1 )}

x \leq - 2 or 1 < x \leq 2

Interval Notation

(- \infty, - 2] \cup (1, 2]

Decimal Notation

x \leq - 1.41421 \dots or 1 < x \leq 1.41421 \dots

Solution steps

x + 1 \leq \frac{1}{x - 1}

Rewrite in standard form

\frac{x ^{2} - 2}{x - 1} \leq 0

Factor

\frac{x ^{2} - 2}{x - 1} : \frac{( x + 2 ) ( x - 2 )}{x - 1}

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

Identify the intervals

x \leq - 2 or 1 < x \leq 2

(x - 8) (x - 7) < 0

\frac{( x ^{2} + 4 )}{( 5 x )} \geq 1 x

1 - x^{3} < 0

2 > \frac{( 6 x + 28 )}{( x + 2 )}

\frac{( e ) ( x ^{2} - 7 x + 12 )}{( 2 x ^{2} + 4 x + 5 )} > \frac{1}{2}

What is x+1<= 1/((x-1)) ?
The solution to x+1<= 1/((x-1)) is x<=-sqrt(2)\lor 1<x<= sqrt(2)