Solve (4x^2 x - 2) : (x^2)

Question

Simplify the expression

\frac{4 x ^{3} - 2}{x ^{2}}

Evaluate

(4 x^{2} \times x - 2) \div x^{2}

Multiply

More Steps

Multiply the terms

4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

4 x^{2 + 1}

Add the numbers

4 x^{3}

(4 x^{3} - 2) \div x^{2}

Solution

\frac{4 x ^{3} - 2}{x ^{2}}

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Find the excluded values

x = 0

Evaluate

(4 x^{2} \times x - 2) \div (x^{2})

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

x^{2} = 0

Solution

x = 0

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Find the roots

x = \frac{3 4}{2}

Alternative Form

x \approx 0.793701

Evaluate

(4 x^{2} \times x - 2) \div (x^{2})

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

(4 x^{2} \times x - 2) \div (x^{2}) = 0

The only way a power can not be 0 is when the base not equals 0

(4 x^{2} \times x - 2) \div (x^{2}) = 0, x \neq = 0

Calculate

(4 x^{2} \times x - 2) \div (x^{2}) = 0

Multiply

More Steps

Multiply the terms

4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

4 x^{2 + 1}

Add the numbers

4 x^{3}

(4 x^{3} - 2) \div (x^{2}) = 0

Calculate

(4 x^{3} - 2) \div x^{2} = 0

Rewrite the expression

\frac{4 x ^{3} - 2}{x ^{2}} = 0

Cross multiply

4 x^{3} - 2 = x^{2} \times 0

Simplify the equation

4 x^{3} - 2 = 0

Move the constant to the right side

4 x^{3} = 2

Divide both sides

\frac{4 x ^{3}}{4} = \frac{2}{4}

Divide the numbers

x^{3} = \frac{2}{4}

Cancel out the common factor 2

x^{3} = \frac{1}{2}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{2}

Calculate

x = 3 \frac{1}{2}

Simplify the root

More Steps

Evaluate

3 \frac{1}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 2}

Simplify the radical expression

\frac{1}{3 2}

Multiply by the Conjugate

\frac{3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

The product of roots with the same index is equal to the root of the product

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 4}{2}

x = \frac{3 4}{2}

Check if the solution is in the defined range

x = \frac{3 4}{2}, x \neq = 0

Solution

x = \frac{3 4}{2}

Alternative Form

x \approx 0.793701

Show Solution