Solve (3x^2 - 6x^3) / (x - 1)

Question

Find the excluded values

x = 1

Evaluate

\frac{3 x ^{2} - 6 x ^{3}}{x - 1}

To find the excluded values,set the denominators equal to 0

x - 1 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 1

Solution

x = 1

Show Solution

- 6 x^{2} - 3 x - 3 + \frac{- 3}{x - 1}

Evaluate

\frac{3 x ^{2} - 6 x ^{3}}{x - 1}

Solution

- 6 x^{2} - 3 x - 3 + \frac{- 3}{x - 1}

Show Solution

x_{1} = 0, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.5

Evaluate

\frac{3 x ^{2} - 6 x ^{3}}{x - 1}

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

\frac{3 x ^{2} - 6 x ^{3}}{x - 1} = 0

Find the domain

More Steps

Evaluate

x - 1 \neq = 0

Move the constant to the right side

x \neq = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

x \neq = 1

\frac{3 x ^{2} - 6 x ^{3}}{x - 1} = 0, x \neq = 1

Calculate

\frac{3 x ^{2} - 6 x ^{3}}{x - 1} = 0

Cross multiply

3 x^{2} - 6 x^{3} = (x - 1) \times 0

Simplify the equation

3 x^{2} - 6 x^{3} = 0

Factor the expression

3 x^{2} (1 - 2 x) = 0

Divide both sides

x^{2} (1 - 2 x) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 2 x = 0

The only way a power can be 0 is when the base equals 0

x = 0 1 - 2 x = 0

Solve the equation

More Steps

Evaluate

1 - 2 x = 0

Move the constant to the right-hand side and change its sign

- 2 x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- 2 x = - 1

Change the signs on both sides of the equation

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 0 x = \frac{1}{2}

Check if the solution is in the defined range

x = 0 x = \frac{1}{2}, x \neq = 1

Find the intersection of the solution and the defined range

x = 0 x = \frac{1}{2}

Solution

x_{1} = 0, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.5

Show Solution