Problem:
x/4 - 4/x = 0
Directions:Solve the rational expression.
x = -4
x = 4
To solve the rational expression x/4 - 4/x = 0, we need to get rid of the fractions first.
To do this, we can multiply every term in the equation by the least common denominator (LCD) of the fractions, which is 4x.
So, multiplying both sides of the equation by 4x gives us:
x(x) - 4(4) = 0
This simplifies to:
x^2 - 16 = 0
Now, we have a quadratic equation x^2 - 16 = 0. We can solve this equation by factoring or using the quadratic formula.
If we factor it:
(x - 4)(x + 4) = 0
This means either x - 4 = 0 or x + 4 = 0.
Solving for x gives us:
x = 4 or x = -4
So, the solutions to the rational expression x/4 - 4/x = 0 are x = 4 and x = -4.