x^2/x-4 - 7/x-4=0

*Please solve the rational expression.

multipy both sides by (x-4)

then you have
x^2-7=0
x= +- sqrt 7

To solve the rational expression x^2/(x-4) - 7/(x-4) = 0, we can start by multiplying both sides of the equation by (x-4). This will help us eliminate the denominators and make the equation easier to solve.

(x^2/(x-4)) * (x-4) - (7/(x-4)) * (x-4) = 0

After multiplying, the equation becomes:

x^2 - 7 = 0

Now, we have a quadratic equation. To solve for x, we can set the equation equal to zero and use factoring or the quadratic formula. In this case, we can notice that the equation is a perfect square trinomial:

(x - √7)(x + √7) = 0

Now, we can solve for x by setting each factor equal to zero:

x - √7 = 0 or x + √7 = 0

Solving for x in each equation gives us:

x = √7 or x = -√7

So the solutions to the rational expression are x = √7 and x = -√7.