Solve (27g^4-327g^290g)/(3g-10)

Question

Simplify the expression

\frac{27 g ^{4} - 29430 g ^{3}}{3 g - 10}

Evaluate

(27 g^{4} - 327 g^{2} \times 90 g) \div (3 g - 10)

Multiply

More Steps

Multiply the terms

327 g^{2} \times 90 g

Multiply the terms

29430 g^{2} \times g

Multiply the terms with the same base by adding their exponents

29430 g^{2 + 1}

Add the numbers

29430 g^{3}

(27 g^{4} - 29430 g^{3}) \div (3 g - 10)

Solution

\frac{27 g ^{4} - 29430 g ^{3}}{3 g - 10}

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Find the excluded values

g = \frac{10}{3}

Evaluate

(27 g^{4} - 327 g^{2} \times 90 g) \div (3 g - 10)

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

3 g - 10 = 0

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

3 g = 0 + 10

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

3 g = 10

Divide both sides

\frac{3 g}{3} = \frac{10}{3}

Solution

g = \frac{10}{3}

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Find the roots

g_{1} = 0, g_{2} = 1090

Evaluate

(27 g^{4} - 327 g^{2} \times 90 g) \div (3 g - 10)

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

(27 g^{4} - 327 g^{2} \times 90 g) \div (3 g - 10) = 0

Find the domain

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Evaluate

3 g - 10 \neq = 0

Move the constant to the right side

3 g \neq = 0 + 10

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

3 g \neq = 10

Divide both sides

\frac{3 g}{3} \neq = \frac{10}{3}

Divide the numbers

g \neq = \frac{10}{3}

(27 g^{4} - 327 g^{2} \times 90 g) \div (3 g - 10) = 0, g \neq = \frac{10}{3}

Calculate

(27 g^{4} - 327 g^{2} \times 90 g) \div (3 g - 10) = 0

Multiply

More Steps

Multiply the terms

327 g^{2} \times 90 g

Multiply the terms

29430 g^{2} \times g

Multiply the terms with the same base by adding their exponents

29430 g^{2 + 1}

Add the numbers

29430 g^{3}

(27 g^{4} - 29430 g^{3}) \div (3 g - 10) = 0

Rewrite the expression

\frac{27 g ^{4} - 29430 g ^{3}}{3 g - 10} = 0

Cross multiply

27 g^{4} - 29430 g^{3} = (3 g - 10) \times 0

Simplify the equation

27 g^{4} - 29430 g^{3} = 0

Factor the expression

27 g^{3} (g - 1090) = 0

Divide both sides

g^{3} (g - 1090) = 0

Separate the equation into 2 possible cases

g^{3} = 0 g - 1090 = 0

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

g = 0 g - 1090 = 0

Solve the equation

More Steps

Evaluate

g - 1090 = 0

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

g = 0 + 1090

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

g = 1090

g = 0 g = 1090

Check if the solution is in the defined range

g = 0 g = 1090, g \neq = \frac{10}{3}

Find the intersection of the solution and the defined range

g = 0 g = 1090

Solution

g_{1} = 0, g_{2} = 1090

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