What is (4x^2)/(x^2+5)<1 ?

The solution to (4x^2)/(x^2+5)<1 is -sqrt(5/3)<x<sqrt(5/3)

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(4x^2)/(x^2+5)<1

\frac{4 x ^{2}}{x ^{2} + 5} < 1

- \frac{5}{3} < x < \frac{5}{3}

Interval Notation

(- \frac{5}{3}, \frac{5}{3})

Decimal Notation

- 1.29099 \dots < x < 1.29099 \dots

Solution steps

\frac{4 x ^{2}}{x ^{2} + 5} < 1

Rewrite in standard form

\frac{3 x ^{2} - 5}{x ^{2} + 5} < 0

Factor

\frac{3 x ^{2} - 5}{x ^{2} + 5} : \frac{( 3 x + 5 ) ( 3 x - 5 )}{x ^{2} + 5}

\frac{( 3 x + 5 ) ( 3 x - 5 )}{x ^{2} + 5} < 0

Identify the intervals

- \frac{5}{3} < x < \frac{5}{3}

5 x^{2} - 8 x - 4

x (x + 5) = x + 77

1 - \frac{1}{1 - a}

4 z^{2} + 29 = 24 z

x^{2} + 6 + 9 = 0

What is (4x^2)/(x^2+5)<1 ?
The solution to (4x^2)/(x^2+5)<1 is -sqrt(5/3)<x<sqrt(5/3)