Solve (2d^2-14d^32)/(d-6)

Question

Simplify the expression

\frac{2 d ^{2} - 28 d ^{3}}{d - 6}

Evaluate

\frac{2 d ^{2} - 14 d ^{3} \times 2}{d - 6}

Solution

\frac{2 d ^{2} - 28 d ^{3}}{d - 6}

Show Solution

d = 6

Evaluate

\frac{2 d ^{2} - 14 d ^{3} \times 2}{d - 6}

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

d - 6 = 0

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

d = 0 + 6

Solution

d = 6

Show Solution

d_{1} = 0, d_{2} = \frac{1}{14}

Alternative Form

d_{1} = 0, d_{2} = 0.0 \dot{7} 1428 \dot{5}

Evaluate

\frac{2 d ^{2} - 14 d ^{3} \times 2}{d - 6}

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

\frac{2 d ^{2} - 14 d ^{3} \times 2}{d - 6} = 0

Find the domain

More Steps

Evaluate

d - 6 \neq = 0

Move the constant to the right side

d \neq = 0 + 6

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

d \neq = 6

\frac{2 d ^{2} - 14 d ^{3} \times 2}{d - 6} = 0, d \neq = 6

Calculate

\frac{2 d ^{2} - 14 d ^{3} \times 2}{d - 6} = 0

Multiply the terms

\frac{2 d ^{2} - 28 d ^{3}}{d - 6} = 0

Cross multiply

2 d^{2} - 28 d^{3} = (d - 6) \times 0

Simplify the equation

2 d^{2} - 28 d^{3} = 0

Factor the expression

2 d^{2} (1 - 14 d) = 0

Divide both sides

d^{2} (1 - 14 d) = 0

Separate the equation into 2 possible cases

d^{2} = 0 1 - 14 d = 0

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

d = 0 1 - 14 d = 0

Solve the equation

More Steps

Evaluate

1 - 14 d = 0

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

- 14 d = 0 - 1

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

- 14 d = - 1

Change the signs on both sides of the equation

14 d = 1

Divide both sides

\frac{14 d}{14} = \frac{1}{14}

Divide the numbers

d = \frac{1}{14}

d = 0 d = \frac{1}{14}

Check if the solution is in the defined range

d = 0 d = \frac{1}{14}, d \neq = 6

Find the intersection of the solution and the defined range

d = 0 d = \frac{1}{14}

Solution

d_{1} = 0, d_{2} = \frac{1}{14}

Alternative Form

d_{1} = 0, d_{2} = 0.0 \dot{7} 1428 \dot{5}

Show Solution