Solve (-5x^326x^2-33x)/(x-3)

Question

Simplify the expression

- \frac{130 x ^{5} + 33 x}{x - 3}

Evaluate

\frac{- 5 x ^{3} \times 26 x ^{2} - 33 x}{x - 3}

Multiply

More Steps

Multiply the terms

- 5 x^{3} \times 26 x^{2}

Multiply the terms

- 130 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 130 x^{3 + 2}

Add the numbers

- 130 x^{5}

\frac{- 130 x ^{5} - 33 x}{x - 3}

Solution

- \frac{130 x ^{5} + 33 x}{x - 3}

Show Solution

x = 3

Evaluate

\frac{- 5 x ^{3} \times 26 x ^{2} - 33 x}{x - 3}

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

x - 3 = 0

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

x = 0 + 3

Solution

x = 3

Show Solution

x = 0

Evaluate

\frac{- 5 x ^{3} \times 26 x ^{2} - 33 x}{x - 3}

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

\frac{- 5 x ^{3} \times 26 x ^{2} - 33 x}{x - 3} = 0

Find the domain

More Steps

Evaluate

x - 3 \neq = 0

Move the constant to the right side

x \neq = 0 + 3

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

x \neq = 3

\frac{- 5 x ^{3} \times 26 x ^{2} - 33 x}{x - 3} = 0, x \neq = 3

Calculate

\frac{- 5 x ^{3} \times 26 x ^{2} - 33 x}{x - 3} = 0

Multiply

More Steps

Multiply the terms

- 5 x^{3} \times 26 x^{2}

Multiply the terms

- 130 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 130 x^{3 + 2}

Add the numbers

- 130 x^{5}

\frac{- 130 x ^{5} - 33 x}{x - 3} = 0

Cross multiply

- 130 x^{5} - 33 x = (x - 3) \times 0

Simplify the equation

- 130 x^{5} - 33 x = 0

Factor the expression

- x (130 x^{4} + 33) = 0

Divide both sides

x (130 x^{4} + 33) = 0

Separate the equation into 2 possible cases

x = 0 130 x^{4} + 33 = 0

Solve the equation

More Steps

Evaluate

130 x^{4} + 33 = 0

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

130 x^{4} = 0 - 33

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

130 x^{4} = - 33

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x

x \in / R

x = 0 x \in / R

Find the union

x = 0

Check if the solution is in the defined range

x = 0, x \neq = 3

Solution

x = 0

Show Solution