Solve \frac{1}{\:x} \frac{1}{3x}=\frac{8}{9}

Question

Solve the equation

x_{1} = - \frac{6}{4}, x_{2} = \frac{6}{4}

Alternative Form

x_{1} \approx - 0.612372, x_{2} \approx 0.612372

Evaluate

\frac{1}{x} \times \frac{1}{3 x} = \frac{8}{9}

Find the domain

More Steps

\frac{1}{x} \times \frac{1}{3 x} = \frac{8}{9}, x \neq = 0

Multiply the terms

More Steps

\frac{1}{3 x ^{2}} = \frac{8}{9}

Rewrite the expression

3 x^{2} = \frac{9}{8}

Multiply by the reciprocal

3 x^{2} \times \frac{1}{3} = \frac{9}{8} \times \frac{1}{3}

Multiply

x^{2} = \frac{9}{8} \times \frac{1}{3}

Multiply

More Steps

x^{2} = \frac{3}{8}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{3}{8}

Simplify the expression

More Steps

x = \pm \frac{6}{4}

Separate the equation into 2 possible cases

x = \frac{6}{4} x = - \frac{6}{4}

Check if the solution is in the defined range

x = \frac{6}{4} x = - \frac{6}{4}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{6}{4} x = - \frac{6}{4}

Solution

x_{1} = - \frac{6}{4}, x_{2} = \frac{6}{4}

Alternative Form

x_{1} \approx - 0.612372, x_{2} \approx 0.612372

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