What is the answer to x/(2sqrt(x^2+9))-1/3 =0 ?

The answer to x/(2sqrt(x^2+9))-1/3 =0 is x= 6/(sqrt(5))

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x/(2sqrt(x^2+9))-1/3 =0

\frac{x}{2 x ^{2} + 9} - \frac{1}{3} = 0

x = \frac{6}{5}

Decimal Notation

x = 2.68328 \dots

Solution steps

\frac{x}{2 x ^{2} + 9} - \frac{1}{3} = 0

Find Least Common Multiplier of

2 x^{2} + 9, 3 : 6 x^{2} + 9

Multiply by LCM=

6 x^{2} + 9

\frac{x}{2 x ^{2} + 9} \cdot 6 x^{2} + 9 - \frac{1}{3} \cdot 6 x^{2} + 9 = 0 \cdot 6 x^{2} + 9

Simplify

3 x - 2 x^{2} + 9 = 0

Remove square roots

4 x^{2} + 36 = 9 x^{2}

Solve

4 x^{2} + 36 = 9 x^{2} : x = \frac{6}{5}, x = - \frac{6}{5}

x = \frac{6}{5}, x = - \frac{6}{5}

Verify Solutions:

x = \frac{6}{5}

True

, x = - \frac{6}{5}

False

The solution is

x = \frac{6}{5}

a^{2} + x^{2}

k = 1 + 3 k - 5

x + 3 + x = 9

7 - p - 9 = - 5

\frac{5 x - 2}{3 x ^{\frac{1}{3}}} = 0

What is the answer to x/(2sqrt(x^2+9))-1/3 =0 ?
The answer to x/(2sqrt(x^2+9))-1/3 =0 is x= 6/(sqrt(5))
Solve for x: x/(2sqrt(x^2+9))-1/3 =0
The solution is x= 6/(sqrt(5))