What is (x^2-1)/(-x^2+2x-1)<= 0 ?

The solution to (x^2-1)/(-x^2+2x-1) 1

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(x^2-1)/(-x^2+2x-1)<= 0

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

x \leq - 1 or x > 1

Interval Notation

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

Solution steps

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

\frac{( x + 1 ) ( x - 1 ) ( - 1 )}{- ( x - 1 ) ^{2}} \geq 0 \cdot (- 1)

Simplify

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

\frac{x + 1}{x - 1} \geq 0

Identify the intervals

x \leq - 1 or x > 1

(x + 2)^{2} + 8 (x + 2) - 20 = 0

2 x^{2} + 5 x - 42 = 0

- \frac{7}{- 3}

\frac{85}{5}

(3 x + 2)^{4} - 4 (3 x + 2)^{2}

What is (x^2-1)/(-x^2+2x-1)<= 0 ?
The solution to (x^2-1)/(-x^2+2x-1)<= 0 is x<=-1\lor x>1