Question

How do you solve `3/(x-3)=x/(x-3)-3/2`?

Answer 1

x=3

Explanation:

Suggestion, take `x/(x-3)` and throw it to the left side as you can see they have a common denominator. This gives you:
`3/(x-3) - x/(x-3)` = `-3/2`
`(3-x)/(x-3) = -3/2`.
Now, you cross-multiply the right and left sides.
`2*(3-x) = -3*(x-3)`
`6 - 2x = -3x + 9` (Just open the brackets)
Now, rearrange terms: `-2x + 3x = 9-6`
Which gives x = 3