Solve 1/x^2/3=1/5

Question

Solve the equation

x_{1} = - \frac{15}{3}, x_{2} = \frac{15}{3}

Alternative Form

x_{1} \approx - 1.290994, x_{2} \approx 1.290994

Evaluate

\frac{1}{x ^{2}} \div 3 = \frac{1}{5}

Find the domain

More Steps

Evaluate

x^{2} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

\frac{1}{x ^{2}} \div 3 = \frac{1}{5}, x \neq = 0

Divide the terms

More Steps

Evaluate

\frac{1}{x ^{2}} \div 3

Multiply by the reciprocal

\frac{1}{x ^{2}} \times \frac{1}{3}

Multiply the terms

\frac{1}{x ^{2} \times 3}

Use the commutative property to reorder the terms

\frac{1}{3 x ^{2}}

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

Rewrite the expression

3 x^{2} = 5

Divide both sides

\frac{3 x ^{2}}{3} = \frac{5}{3}

Divide the numbers

x^{2} = \frac{5}{3}

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

x = \pm \frac{5}{3}

Simplify the expression

More Steps

Evaluate

\frac{5}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5}{3}

Multiply by the Conjugate

\frac{5 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

5 \times 3

The product of roots with the same index is equal to the root of the product

5 \times 3

Calculate the product

15

\frac{15}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{15}{3}

x = \pm \frac{15}{3}

Separate the equation into 2 possible cases

x = \frac{15}{3} x = - \frac{15}{3}

Check if the solution is in the defined range

x = \frac{15}{3} x = - \frac{15}{3}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{15}{3} x = - \frac{15}{3}

Solution

x_{1} = - \frac{15}{3}, x_{2} = \frac{15}{3}

Alternative Form

x_{1} \approx - 1.290994, x_{2} \approx 1.290994

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