Question

How do you solve `(3x)/( x-5) = 5 - 5 / (x-5)=15`?

Answer 1

No solution

Explanation:

Given equality:

`\frac{3x}{x-5}=5-\frac{5}{x-5}=15`

`\frac{3x}{x-5}=\frac{5x-30}{x-5}=15`

1) Consider

`\frac{3x}{x-5}=\frac{5x-30}{x-5}`

`\frac{3x}{x-5}-\frac{5x-30}{x-5}=0`

`\frac{3x-5x+30}{x-5}=0`

`\frac{-2x+30}{x-5}=0`

`-2x+30=0\ \quad (\forall \ x\ne 5)`

`2x=30`

`x=15`

2) Consider

`\frac{3x}{x-5}=15`

`x=5(x-5)`

`4x=25`

`x=25/4`

`x=6.25`

3) Consider

`\frac{5x-30}{x-5}=15`

`5x-30=15(x-5)`

`10x=45`

`x=4.5`

Since, the values of `x` in all three cases are different hence the given equality doesn't have any solution