# How do you solve the rational equation #x^2/(x-3) - 5/(x-3) = 0#?

First, notice that the denominator is the same for both terms, so we can combine the numerator over the common denominator.

Now we are left with;

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To solve the rational equation x^2/(x-3) - 5/(x-3) = 0, we can combine the fractions on the left side by finding a common denominator. In this case, the common denominator is (x-3).

After combining the fractions, we have (x^2 - 5)/(x-3) = 0.

To solve for x, we can set the numerator equal to zero: x^2 - 5 = 0.

Next, we can factor the quadratic equation: (x - √5)(x + √5) = 0.

Setting each factor equal to zero, we have two possible solutions: x - √5 = 0 or x + √5 = 0.

Solving for x in each equation, we get x = √5 or x = -√5.

Therefore, the solutions to the rational equation x^2/(x-3) - 5/(x-3) = 0 are x = √5 and x = -√5.

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