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

1 Answer
Jan 15, 2016

x= +-sqrt5

Explanation:

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.

(x^2 - 5)/(x-3) = 0

Now we need to contend with the x in the denominator. We can multiply both sides of the equation by (x-3). The left hand side cancels the denominator, and the right hand side multiplies by zero.

(x^2-5)cancel((x-3)/(x-3))^1 = 0cancel((x-3))^0

Now we are left with;

x^2-5 = 0

We only have one x term and a constant, so lets add 5 to both sides.

x^2 = 5

Now we just need to get rid of the exponent. We can take the square root of both sides to get our x values;

x= +-sqrt5