Solve (6g^3-20g^26g)/(g-3)

Question

Simplify the expression

- \frac{114 g ^{3}}{g - 3}

Evaluate

\frac{6 g ^{3} - 20 g ^{2} \times 6 g}{g - 3}

Multiply

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Multiply the terms

20 g^{2} \times 6 g

Multiply the terms

120 g^{2} \times g

Multiply the terms with the same base by adding their exponents

120 g^{2 + 1}

Add the numbers

120 g^{3}

\frac{6 g ^{3} - 120 g ^{3}}{g - 3}

Subtract the terms

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Simplify

6 g^{3} - 120 g^{3}

Collect like terms by calculating the sum or difference of their coefficients

(6 - 120) g^{3}

Subtract the numbers

- 114 g^{3}

\frac{- 114 g ^{3}}{g - 3}

Solution

- \frac{114 g ^{3}}{g - 3}

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Find the excluded values

g = 3

Evaluate

\frac{6 g ^{3} - 20 g ^{2} \times 6 g}{g - 3}

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

g - 3 = 0

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

g = 0 + 3

Solution

g = 3

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Find the roots

g = 0

Evaluate

\frac{6 g ^{3} - 20 g ^{2} \times 6 g}{g - 3}

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

\frac{6 g ^{3} - 20 g ^{2} \times 6 g}{g - 3} = 0

Find the domain

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Evaluate

g - 3 \neq = 0

Move the constant to the right side

g \neq = 0 + 3

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

g \neq = 3

\frac{6 g ^{3} - 20 g ^{2} \times 6 g}{g - 3} = 0, g \neq = 3

Calculate

\frac{6 g ^{3} - 20 g ^{2} \times 6 g}{g - 3} = 0

Multiply

More Steps

Multiply the terms

20 g^{2} \times 6 g

Multiply the terms

120 g^{2} \times g

Multiply the terms with the same base by adding their exponents

120 g^{2 + 1}

Add the numbers

120 g^{3}

\frac{6 g ^{3} - 120 g ^{3}}{g - 3} = 0

Subtract the terms

More Steps

Simplify

6 g^{3} - 120 g^{3}

Collect like terms by calculating the sum or difference of their coefficients

(6 - 120) g^{3}

Subtract the numbers

- 114 g^{3}

\frac{- 114 g ^{3}}{g - 3} = 0

Cross multiply

- 114 g^{3} = (g - 3) \times 0

Simplify the equation

- 114 g^{3} = 0

Change the signs on both sides of the equation

114 g^{3} = 0

Rewrite the expression

g^{3} = 0

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

g = 0

Check if the solution is in the defined range

g = 0, g \neq = 3

Solution

g = 0

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