Question

How do you solve `\frac { 1} { x - 3} = \frac { 3} { x } - \frac { 3} { x - 3}`?

Answer 1

First you need to get a common denominator. In this case it would be `x^2 -3x`.

Explanation:

To get the term 1/(x-3) to have the common denominator, you need to multiply the numerator and the denominator by x. To get the term 3/x to have the common denominator, multiply the numerator and the denominator by x-3. To get the term 3/(x-3) to have the common denominator, multiply the numerator and the denominator by x.
Then you end up with:
`x/(x^2 -3x) = [(3x-9)/(x^2 -3x)] - [(3x)/(x^2 -3x)]`

Next, combine the two terms on the right of the equals sign.
You end up with:
`x/(x^2 -3x) = -9/(x^2 -3x)`

Then you have to multiply the entire equation by `x^2 -3x`, so you can get rid of the denominator by cancelling.
`x^2 -3x*[x/(x^2 -3x) = -9/(x^2 -3x)]`

`x=-9`
Hope this helps :)