Question

How do you solve `(2x)/(x-4)=8/(x-4)+3`?

Answer 1

No solution!

Explanation:

First, note that 4 cannot be a solution (division by zero)

Then, multiply both sides by `(x-4)`, you get

`2x = 8+3*(x-4)`
`=> 3x-2x= 3*4-8`
`=> x = 4` which is impossible!
So there is no solution

Answer 2

The equation is unsolvable.

Explanation:

We have:

`(2x)/(x-4) = 8/(x-4)+3`

Multiply all terms by `x-4`.

`2x=8+3(x-4)`

Expand the brackets.

`2x=8+3x-12=3x-4`

Add `4-2x` to both sides.

`4=x` or `x=4`

Unfortunately this leads to a problem that `x=4` is a singularity (mathematicians don't like infinities).

Reorganise the original equation by subtracting `8/(x-4)` from both sides.

`(2x-8)/(x-4)=3`

This gives:

`(2(x-4))/(x-4)=3`

This gives `2=3` the equation makes no sense unless `x=4` in which case both sides are infinite..