Solve x 1/x-5=1/x^3 - ScanMath

HOME CALCULATOR

DOWNLOAD FOR FREE

Algebra
Calculus
Trigonometry
Matrix

Type your math problem... x 1/x-5=1/x^3

Question

Solve the equation

x = - \frac{3 2}{2}

Alternative Form

x \approx - 0.629961

Evaluate

x \times \frac{1}{x} - 5 = \frac{1}{x ^{3}}

Find the domain

More Steps

x \times \frac{1}{x} - 5 = \frac{1}{x ^{3}}, x \neq = 0

Simplify

More Steps

- 4 = \frac{1}{x ^{3}}

Swap the sides of the equation

\frac{1}{x ^{3}} = - 4

Cross multiply

1 = x^{3} (- 4)

Simplify the equation

1 = - 4 x^{3}

Swap the sides of the equation

- 4 x^{3} = 1

Change the signs on both sides of the equation

4 x^{3} = - 1

Divide both sides

\frac{4 x ^{3}}{4} = \frac{- 1}{4}

Divide the numbers

x^{3} = \frac{- 1}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{1}{4}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{1}{4}

Calculate

x = 3 - \frac{1}{4}

Simplify the root

More Steps

x = - \frac{3 2}{2}

Check if the solution is in the defined range

x = - \frac{3 2}{2}, x \neq = 0

Solution

x = - \frac{3 2}{2}

Alternative Form

x \approx - 0.629961

Show Solution

Graph

Graph