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Popular >

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

Solution

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

Solution

True for all x

+1

Interval Notation

(- \infty, \infty)

Solution steps

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

If

\frac{1}{a} < 0

then

a < 0

x - x^{2} - 1 < 0

Complete the square

x - x^{2} - 1 : - (x - \frac{1}{2})^{2} - \frac{3}{4}

- (x - \frac{1}{2})^{2} - \frac{3}{4} < 0

Move

\frac{3}{4}

to the right side

- (x - \frac{1}{2})^{2} < \frac{3}{4}

Multiply both sides by

- 1

(x - \frac{1}{2})^{2} > - \frac{3}{4}

If n is even,

u^{n} \geq 0

for all

u

True for all x

Popular Examples

1/x < 2/((x-2))

\frac{1}{x} < \frac{2}{( x - 2 )}

x^{4} - x^{2} < 0

\frac{3}{( x - 2 )} < 1

((x^3*(x-2)(5-x)))/(((x^2-4)(x+1)))>0

\frac{( x ^{3} \cdot ( x - 2 ) ( 5 - x ) )}{( ( x ^{2} - 4 ) ( x + 1 ) )} > 0

\frac{2}{( x - 3 )} < 0

Frequently Asked Questions (FAQ)

What is 1/((x-x^2-1))<0 ?
The solution to 1/((x-x^2-1))<0 is True for all x