Solve 3/4(t^(4/3))-3/4(t^(-2/3))

Question

Simplify the expression

\frac{3 t ^{2} 3 t - 3 3 t}{4 t}

Show Solution

t_{1} = - 1, t_{2} = 1

Evaluate

\frac{3}{4} (t^{\frac{4}{3}}) - \frac{3}{4} (t^{- \frac{2}{3}})

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

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

Find the domain

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

Calculate

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

Calculate

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

Calculate

\frac{3}{4} t^{\frac{4}{3}} - \frac{3}{4} t^{- \frac{2}{3}} = 0

Rewrite the expression

More Steps

\frac{3}{4} t^{\frac{4}{3}} - \frac{3}{4 t ^{\frac{2}{3}}} = 0

Multiply both sides of the equation by LCD

(\frac{3}{4} t^{\frac{4}{3}} - \frac{3}{4 t ^{\frac{2}{3}}}) \times 4 t^{\frac{2}{3}} = 0 \times 4 t^{\frac{2}{3}}

Simplify the equation

More Steps

3 t^{2} - 3 = 0 \times 4 t^{\frac{2}{3}}

Any expression multiplied by 0 equals 0

3 t^{2} - 3 = 0

Move the constant to the right side

3 t^{2} = 3

Divide both sides

\frac{3 t ^{2}}{3} = \frac{3}{3}

Divide the numbers

t^{2} = \frac{3}{3}

Divide the numbers

More Steps

t^{2} = 1

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

t = \pm 1

Simplify the expression

t = \pm 1

Separate the equation into 2 possible cases

t = 1 t = - 1

Check if the solution is in the defined range

t = 1 t = - 1, t \neq = 0

Find the intersection of the solution and the defined range

t = 1 t = - 1

Solution

t_{1} = - 1, t_{2} = 1

Show Solution