Solve (x^(3)-13x^(2) 40x 14)/(x-7)

Question

Simplify the expression

- \frac{7279 x ^{3}}{x - 7}

Evaluate

\frac{x ^{3} - 13 x ^{2} \times 40 x \times 14}{x - 7}

Multiply

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Multiply the terms

13 x^{2} \times 40 x \times 14

Multiply the terms

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Evaluate

13 \times 40 \times 14

Multiply the terms

520 \times 14

Multiply the numbers

7280

7280 x^{2} \times x

Multiply the terms with the same base by adding their exponents

7280 x^{2 + 1}

Add the numbers

7280 x^{3}

\frac{x ^{3} - 7280 x ^{3}}{x - 7}

Subtract the terms

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Simplify

x^{3} - 7280 x^{3}

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

(1 - 7280) x^{3}

Subtract the numbers

- 7279 x^{3}

\frac{- 7279 x ^{3}}{x - 7}

Solution

- \frac{7279 x ^{3}}{x - 7}

Show Solution

Find the excluded values

x = 7

Evaluate

\frac{x ^{3} - 13 x ^{2} \times 40 x \times 14}{x - 7}

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

x - 7 = 0

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

x = 0 + 7

Solution

x = 7

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Find the roots

x = 0

Evaluate

\frac{x ^{3} - 13 x ^{2} \times 40 x \times 14}{x - 7}

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

\frac{x ^{3} - 13 x ^{2} \times 40 x \times 14}{x - 7} = 0

Find the domain

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Evaluate

x - 7 \neq = 0

Move the constant to the right side

x \neq = 0 + 7

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

x \neq = 7

\frac{x ^{3} - 13 x ^{2} \times 40 x \times 14}{x - 7} = 0, x \neq = 7

Calculate

\frac{x ^{3} - 13 x ^{2} \times 40 x \times 14}{x - 7} = 0

Multiply

More Steps

Multiply the terms

13 x^{2} \times 40 x \times 14

Multiply the terms

More Steps

Evaluate

13 \times 40 \times 14

Multiply the terms

520 \times 14

Multiply the numbers

7280

7280 x^{2} \times x

Multiply the terms with the same base by adding their exponents

7280 x^{2 + 1}

Add the numbers

7280 x^{3}

\frac{x ^{3} - 7280 x ^{3}}{x - 7} = 0

Subtract the terms

More Steps

Simplify

x^{3} - 7280 x^{3}

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

(1 - 7280) x^{3}

Subtract the numbers

- 7279 x^{3}

\frac{- 7279 x ^{3}}{x - 7} = 0

Cross multiply

- 7279 x^{3} = (x - 7) \times 0

Simplify the equation

- 7279 x^{3} = 0

Change the signs on both sides of the equation

7279 x^{3} = 0

Rewrite the expression

x^{3} = 0

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

x = 0

Check if the solution is in the defined range

x = 0, x \neq = 7

Solution

x = 0

Show Solution