Final answer:
To find the vertical asymptotes of the given function, set the denominator equal to zero and solve for x. The vertical asymptotes are the values of x that make the denominator zero, which in this case are x = 0 and x = 9/5.
Step-by-step explanation:
To find the vertical asymptotes of the function y = x² + 1/5x - 2x², we need to consider the values of x that make the denominator of the function equal to zero.
In this case, the denominator is x² - 2x² + 1/5x. To find the values of x that make this denominator equal to zero, we can set it equal to zero and solve for x.
x² - 2x² + 1/5x = 0
To solve this quadratic equation, we can factor out x:
x(x - 2 + 1/5) = 0
So, we have x(x - 9/5) = 0
This equation has two solutions: x = 0 and x = 9/5.
Therefore, the vertical asymptotes of the function y = x² + 1/5x - 2x² are x = 0 and x = 9/5.