What is (4x^2)/(x^2+6)<1 ?

The solution to (4x^2)/(x^2+6)<1 is -sqrt(2)<x<sqrt(2)

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(4x^2)/(x^2+6)<1

\frac{4 x ^{2}}{x ^{2} + 6} < 1

- 2 < x < 2

Interval Notation

(- 2, 2)

Decimal Notation

- 1.41421 \dots < x < 1.41421 \dots

Solution steps

\frac{4 x ^{2}}{x ^{2} + 6} < 1

Rewrite in standard form

\frac{3 x ^{2} - 6}{x ^{2} + 6} < 0

Factor

\frac{3 x ^{2} - 6}{x ^{2} + 6} : \frac{3 ( x + 2 ) ( x - 2 )}{x ^{2} + 6}

\frac{3 ( x + 2 ) ( x - 2 )}{x ^{2} + 6} < 0

Divide both sides by

3

\frac{\frac{3 ( x + 2 ) ( x - 2 )}{x ^{2} + 6}}{3} < \frac{0}{3}

Simplify

\frac{( x + 2 ) ( x - 2 )}{x ^{2} + 6} < 0

Identify the intervals

- 2 < x < 2

100 x^{2} + 19.62 x - 60.76 = 0

6 (x + 12) = - 42

12 m^{2} - 24 m - 15

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

1^{2} + x^{2} = 4^{2}

What is (4x^2)/(x^2+6)<1 ?
The solution to (4x^2)/(x^2+6)<1 is -sqrt(2)<x<sqrt(2)