What is 4/(x^2-1)>1 ?

The solution to 4/(x^2-1)>1 is -sqrt(5)<x<-1\lor 1<x<sqrt(5)

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4/(x^2-1)>1

\frac{4}{x ^{2} - 1} > 1

- 5 < x < - 1 or 1 < x < 5

Interval Notation

(- 5, - 1) \cup (1, 5)

Decimal Notation

- 2.23606 \dots < x < - 1 or 1 < x < 2.23606 \dots

Solution steps

\frac{4}{x ^{2} - 1} > 1

Rewrite in standard form

\frac{- x ^{2} + 5}{x ^{2} - 1} > 0

Factor

\frac{- x ^{2} + 5}{x ^{2} - 1} : \frac{- ( x + 5 ) ( x - 5 )}{( x + 1 ) ( x - 1 )}

\frac{- ( x + 5 ) ( x - 5 )}{( x + 1 ) ( x - 1 )} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 5 ) ( x - 5 ) ) ( - 1 )}{( x + 1 ) ( x - 1 )} < 0 \cdot (- 1)

Simplify

\frac{( x + 5 ) ( x - 5 )}{( x + 1 ) ( x - 1 )} < 0

Identify the intervals

- 5 < x < - 1 or 1 < x < 5

\frac{7}{8} - \frac{3}{4}

(x - 7)^{2} - 75 = 0

\frac{2}{3} x^{2} + \frac{1}{4} x = 3

2 y^{2} + 11 y + 12

(6 + 8 i) (6 - 8 i)

What is 4/(x^2-1)>1 ?
The solution to 4/(x^2-1)>1 is -sqrt(5)<x<-1\lor 1<x<sqrt(5)