Solve \:\frac{-3x^3-11x^2 31x-27}{3x^3 11x^2 x-5}

Question

Simplify the expression

- \frac{344 x ^{3} + 27}{33 x ^{6} - 5}

Show Solution

x = \frac{6 5 \times 3 3 ^{5}}{33}, x = - \frac{6 5 \times 3 3 ^{5}}{33}

Show Solution

x = - \frac{3 3 1849}{86}

Alternative Form

x \approx - 0.428156

Evaluate

\frac{- 3 x ^{3} - 11 x ^{2} \times 31 x - 27}{3 x ^{3} \times 11 x ^{2} \times x - 5}

To find the roots of the expression,set the expression equal to 0

\frac{- 3 x ^{3} - 11 x ^{2} \times 31 x - 27}{3 x ^{3} \times 11 x ^{2} \times x - 5} = 0

Find the domain

More Steps

\frac{- 3 x ^{3} - 11 x ^{2} \times 31 x - 27}{3 x ^{3} \times 11 x ^{2} \times x - 5} = 0, x \in (- \infty, - \frac{6 5 \times 3 3 ^{5}}{33}) \cup (- \frac{6 5 \times 3 3 ^{5}}{33}, \frac{6 5 \times 3 3 ^{5}}{33}) \cup (\frac{6 5 \times 3 3 ^{5}}{33}, + \infty)

Calculate

\frac{- 3 x ^{3} - 11 x ^{2} \times 31 x - 27}{3 x ^{3} \times 11 x ^{2} \times x - 5} = 0

Multiply

More Steps

\frac{- 3 x ^{3} - 341 x ^{3} - 27}{3 x ^{3} \times 11 x ^{2} \times x - 5} = 0

Subtract the terms

More Steps

\frac{- 344 x ^{3} - 27}{3 x ^{3} \times 11 x ^{2} \times x - 5} = 0

Multiply

More Steps

\frac{- 344 x ^{3} - 27}{33 x ^{6} - 5} = 0

Cross multiply

- 344 x^{3} - 27 = (33 x^{6} - 5) \times 0

Simplify the equation

- 344 x^{3} - 27 = 0

Move the constant to the right side

- 344 x^{3} = 27

Change the signs on both sides of the equation

344 x^{3} = - 27

Divide both sides

\frac{344 x ^{3}}{344} = \frac{- 27}{344}

Divide the numbers

x^{3} = \frac{- 27}{344}

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

x^{3} = - \frac{27}{344}

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

3 x^{3} = 3 - \frac{27}{344}

Calculate

x = 3 - \frac{27}{344}

Simplify the root

More Steps

x = - \frac{3 3 1849}{86}

Check if the solution is in the defined range

x = - \frac{3 3 1849}{86}, x \in (- \infty, - \frac{6 5 \times 3 3 ^{5}}{33}) \cup (- \frac{6 5 \times 3 3 ^{5}}{33}, \frac{6 5 \times 3 3 ^{5}}{33}) \cup (\frac{6 5 \times 3 3 ^{5}}{33}, + \infty)

Solution

x = - \frac{3 3 1849}{86}

Alternative Form

x \approx - 0.428156

Show Solution