How do you solve the rational equation #x^2/(x - 4) - 7/(x-4) = 0#?

We can eliminate the denominators

Factor as a difference of squares:

(x + √7)(x - √7) = 0

x = -√7 and √7

To solve the rational equation x^2/(x - 4) - 7/(x-4) = 0, we can start by finding a common denominator for the fractions on the left side, which is (x - 4).

Next, we can combine the fractions by subtracting the second fraction from the first, resulting in (x^2 - 7)/(x - 4) = 0.

Since the numerator is a quadratic expression, we can set it equal to zero and solve for x.

Setting x^2 - 7 = 0, we can add 7 to both sides to get x^2 = 7.

Taking the square root of both sides, we have x = ±√7 as the solutions.

However, we need to check if these solutions make the denominator zero, which would result in an undefined value.

Since x - 4 is the denominator, we need to ensure that x ≠ 4.

Therefore, the solution to the rational equation x^2/(x - 4) - 7/(x-4) = 0 is x = ±√7, where x ≠ 4.