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

Question

Simplify the expression

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

Evaluate

\frac{27 x ^{4} - 327 x ^{2} \times 90 x}{3 x - 10}

Solution

More Steps

Evaluate

327 x^{2} \times 90 x

Multiply the terms

29430 x^{2} \times x

Multiply the terms with the same base by adding their exponents

29430 x^{2 + 1}

Add the numbers

29430 x^{3}

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

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Find the excluded values

x = \frac{10}{3}

Evaluate

\frac{27 x ^{4} - 327 x ^{2} \times 90 x}{3 x - 10}

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

3 x - 10 = 0

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

3 x = 0 + 10

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

3 x = 10

Divide both sides

\frac{3 x}{3} = \frac{10}{3}

Solution

x = \frac{10}{3}

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Find the roots

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

Evaluate

\frac{27 x ^{4} - 327 x ^{2} \times 90 x}{3 x - 10}

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

\frac{27 x ^{4} - 327 x ^{2} \times 90 x}{3 x - 10} = 0

Find the domain

More Steps

Evaluate

3 x - 10 \neq = 0

Move the constant to the right side

3 x \neq = 0 + 10

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

3 x \neq = 10

Divide both sides

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

Divide the numbers

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

\frac{27 x ^{4} - 327 x ^{2} \times 90 x}{3 x - 10} = 0, x \neq = \frac{10}{3}

Calculate

\frac{27 x ^{4} - 327 x ^{2} \times 90 x}{3 x - 10} = 0

Multiply

More Steps

Multiply the terms

327 x^{2} \times 90 x

Multiply the terms

29430 x^{2} \times x

Multiply the terms with the same base by adding their exponents

29430 x^{2 + 1}

Add the numbers

29430 x^{3}

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

Cross multiply

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

Simplify the equation

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

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

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

x = 0 x - 1090 = 0

Solve the equation

More Steps

Evaluate

x - 1090 = 0

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

x = 0 + 1090

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

x = 1090

x = 0 x = 1090

Check if the solution is in the defined range

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

Find the intersection of the solution and the defined range

x = 0 x = 1090

Solution

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

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