What is the answer to x/(2sqrt(x^2+4))-1/3 =0 ?

The answer to x/(2sqrt(x^2+4))-1/3 =0 is x= 4/(sqrt(5))

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x/(2sqrt(x^2+4))-1/3 =0

\frac{x}{2 x ^{2} + 4} - \frac{1}{3} = 0

x = \frac{4}{5}

Decimal Notation

x = 1.78885 \dots

Solution steps

\frac{x}{2 x ^{2} + 4} - \frac{1}{3} = 0

Find Least Common Multiplier of

2 x^{2} + 4, 3 : 6 x^{2} + 4

Multiply by LCM=

6 x^{2} + 4

\frac{x}{2 x ^{2} + 4} \cdot 6 x^{2} + 4 - \frac{1}{3} \cdot 6 x^{2} + 4 = 0 \cdot 6 x^{2} + 4

Simplify

3 x - 2 x^{2} + 4 = 0

Remove square roots

4 x^{2} + 16 = 9 x^{2}

Solve

4 x^{2} + 16 = 9 x^{2} : x = \frac{4}{5}, x = - \frac{4}{5}

x = \frac{4}{5}, x = - \frac{4}{5}

Verify Solutions:

x = \frac{4}{5}

True

, x = - \frac{4}{5}

False

The solution is

x = \frac{4}{5}

x - 4 + x + 4 - 2 x - 1 = 0

x - 3 + x + 5 = \frac{16}{x}

5 x + 44 + 3 = 11

x^{\frac{2}{3}} - 2 x^{\frac{1}{3}} - 3 = 0

What is the answer to x/(2sqrt(x^2+4))-1/3 =0 ?
The answer to x/(2sqrt(x^2+4))-1/3 =0 is x= 4/(sqrt(5))
Solve for x: x/(2sqrt(x^2+4))-1/3 =0
The solution is x= 4/(sqrt(5))