Solve (2x^(2)-5x^4)/(x-1)(x 1)

Question

Simplify the expression

\frac{2 x ^{3} - 5 x ^{5}}{x - 1}

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x = 1

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x_{1} = - \frac{10}{5}, x_{2} = 0, x_{3} = \frac{10}{5}

Alternative Form

x_{1} \approx - 0.632456, x_{2} = 0, x_{3} \approx 0.632456

Evaluate

\frac{2 x ^{2} - 5 x ^{4}}{x - 1} \times (x \times 1)

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

\frac{2 x ^{2} - 5 x ^{4}}{x - 1} \times (x \times 1) = 0

Find the domain

More Steps

\frac{2 x ^{2} - 5 x ^{4}}{x - 1} \times (x \times 1) = 0, x \neq = 1

Calculate

\frac{2 x ^{2} - 5 x ^{4}}{x - 1} \times (x \times 1) = 0

Any expression multiplied by 1 remains the same

\frac{2 x ^{2} - 5 x ^{4}}{x - 1} \times x = 0

Multiply the terms

More Steps

\frac{x ( 2 x ^{2} - 5 x ^{4} )}{x - 1} = 0

Cross multiply

x (2 x^{2} - 5 x^{4}) = (x - 1) \times 0

Simplify the equation

x (2 x^{2} - 5 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 2 x^{2} - 5 x^{4} = 0

Solve the equation

More Steps

x = 0 x = 0 x = \frac{10}{5} x = - \frac{10}{5}

Find the union

x = 0 x = \frac{10}{5} x = - \frac{10}{5}

Check if the solution is in the defined range

x = 0 x = \frac{10}{5} x = - \frac{10}{5}, x \neq = 1

Find the intersection of the solution and the defined range

x = 0 x = \frac{10}{5} x = - \frac{10}{5}

Solution

x_{1} = - \frac{10}{5}, x_{2} = 0, x_{3} = \frac{10}{5}

Alternative Form

x_{1} \approx - 0.632456, x_{2} = 0, x_{3} \approx 0.632456

Show Solution