Question

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

Answer 1

`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`