Solve (5/2) - ((4v)/(3v^3))

Question

Simplify the expression

\frac{15 v ^{2} - 8}{6 v ^{2}}

Show Solution

v = 0

Show Solution

v_{1} = - \frac{2 30}{15}, v_{2} = \frac{2 30}{15}

Alternative Form

v_{1} \approx - 0.730297, v_{2} \approx 0.730297

Evaluate

(\frac{5}{2}) - (\frac{4 v}{3 v ^{3}})

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

(\frac{5}{2}) - (\frac{4 v}{3 v ^{3}}) = 0

Find the domain

More Steps

(\frac{5}{2}) - (\frac{4 v}{3 v ^{3}}) = 0, v \neq = 0

Calculate

(\frac{5}{2}) - (\frac{4 v}{3 v ^{3}}) = 0

Remove the unnecessary parentheses

\frac{5}{2} - (\frac{4 v}{3 v ^{3}}) = 0

Divide the terms

More Steps

\frac{5}{2} - \frac{4}{3 v ^{2}} = 0

Subtract the terms

More Steps

\frac{15 v ^{2} - 8}{6 v ^{2}} = 0

Cross multiply

15 v^{2} - 8 = 6 v^{2} \times 0

Simplify the equation

15 v^{2} - 8 = 0

Move the constant to the right side

15 v^{2} = 8

Divide both sides

\frac{15 v ^{2}}{15} = \frac{8}{15}

Divide the numbers

v^{2} = \frac{8}{15}

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

v = \pm \frac{8}{15}

Simplify the expression

More Steps

v = \pm \frac{2 30}{15}

Separate the equation into 2 possible cases

v = \frac{2 30}{15} v = - \frac{2 30}{15}

Check if the solution is in the defined range

v = \frac{2 30}{15} v = - \frac{2 30}{15}, v \neq = 0

Find the intersection of the solution and the defined range

v = \frac{2 30}{15} v = - \frac{2 30}{15}

Solution

v_{1} = - \frac{2 30}{15}, v_{2} = \frac{2 30}{15}

Alternative Form

v_{1} \approx - 0.730297, v_{2} \approx 0.730297

Show Solution