Solve (2x^(2)-5x^4)/((x-1)⋅(x 1))

Question

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

Simplify the expression

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

Show Solution

x = 0, x = 1

Show Solution

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

Alternative Form

x_{1} \approx - 0.632456, x_{2} \approx 0.632456

Evaluate

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

Find the domain

More Steps

\frac{2 x ^{2} - 5 x ^{4}}{( x - 1 ) ( x \times 1 )} = 0, x \in (- \infty, 0) \cup (0, 1) \cup (1, + \infty)

Calculate

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

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

Divide the terms

More Steps

\frac{2 x - 5 x ^{3}}{x - 1} = 0

Cross multiply

2 x - 5 x^{3} = (x - 1) \times 0

Simplify the equation

2 x - 5 x^{3} = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

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 \in (- \infty, 0) \cup (0, 1) \cup (1, + \infty)

Find the intersection of the solution and the defined range

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

Solution

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

Alternative Form

x_{1} \approx - 0.632456, x_{2} \approx 0.632456

Show Solution