Solve (-2y^33y^29y)/(y-3)

Question

Simplify the expression

- \frac{54 y ^{6}}{y - 3}

Evaluate

\frac{- 2 y ^{3} \times 3 y ^{2} \times 9 y}{y - 3}

Multiply

More Steps

Multiply the terms

- 2 y^{3} \times 3 y^{2} \times 9 y

Multiply the terms

More Steps

Evaluate

2 \times 3 \times 9

Multiply the terms

6 \times 9

Multiply the numbers

54

- 54 y^{3} \times y^{2} \times y

Multiply the terms with the same base by adding their exponents

- 54 y^{3 + 2 + 1}

Add the numbers

- 54 y^{6}

\frac{- 54 y ^{6}}{y - 3}

Solution

- \frac{54 y ^{6}}{y - 3}

Show Solution

y = 3

Evaluate

\frac{- 2 y ^{3} \times 3 y ^{2} \times 9 y}{y - 3}

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

y - 3 = 0

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

y = 0 + 3

Solution

y = 3

Show Solution

y = 0

Evaluate

\frac{- 2 y ^{3} \times 3 y ^{2} \times 9 y}{y - 3}

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

\frac{- 2 y ^{3} \times 3 y ^{2} \times 9 y}{y - 3} = 0

Find the domain

More Steps

Evaluate

y - 3 \neq = 0

Move the constant to the right side

y \neq = 0 + 3

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

y \neq = 3

\frac{- 2 y ^{3} \times 3 y ^{2} \times 9 y}{y - 3} = 0, y \neq = 3

Calculate

\frac{- 2 y ^{3} \times 3 y ^{2} \times 9 y}{y - 3} = 0

Multiply

More Steps

Multiply the terms

- 2 y^{3} \times 3 y^{2} \times 9 y

Multiply the terms

More Steps

Evaluate

2 \times 3 \times 9

Multiply the terms

6 \times 9

Multiply the numbers

54

- 54 y^{3} \times y^{2} \times y

Multiply the terms with the same base by adding their exponents

- 54 y^{3 + 2 + 1}

Add the numbers

- 54 y^{6}

\frac{- 54 y ^{6}}{y - 3} = 0

Cross multiply

- 54 y^{6} = (y - 3) \times 0

Simplify the equation

- 54 y^{6} = 0

Change the signs on both sides of the equation

54 y^{6} = 0

Rewrite the expression

y^{6} = 0

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

y = 0

Check if the solution is in the defined range

y = 0, y \neq = 3

Solution

y = 0

Show Solution