The first step for solving this equation is to determine the defined range. [tex] \frac{ x^{4} }{x-1} = \frac{5}{x-1} [/tex], x ≠ 1 Remember that when the denominators of both fractions are the same,, you need to set the numerators equal. This will look like the following: [tex] x^{4} [/tex] = 5 Take the root of both sides of the equation and remember to use both positive and negative roots. x +/- [tex] \sqrt[4]{5}[/tex] Separate the solutions. x = [tex] \sqrt[4]{5}[/tex] , x ≠ 1 x = -[tex] \sqrt[4]{5}[/tex] Check if the solution is in the defined range. x = [tex] \sqrt[4]{5}[/tex] x = -[tex] \sqrt[4]{5}[/tex] This means that the final solution to your question are the following: x = [tex] \sqrt[4]{5}[/tex] x = -[tex] \sqrt[4]{5}[/tex] Let me know if you have any further questions. :)
