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

No solution

#### Explanation:

Given equality:

$\setminus \frac{3 x}{x - 5} = 5 - \setminus \frac{5}{x - 5} = 15$

$\setminus \frac{3 x}{x - 5} = \setminus \frac{5 x - 30}{x - 5} = 15$

1) Consider

$\setminus \frac{3 x}{x - 5} = \setminus \frac{5 x - 30}{x - 5}$

$\setminus \frac{3 x}{x - 5} - \setminus \frac{5 x - 30}{x - 5} = 0$

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

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

$- 2 x + 30 = 0 \setminus \setminus \quad \left(\setminus \forall \setminus x \setminus \ne 5\right)$

$2 x = 30$

$x = 15$

2) Consider

$\setminus \frac{3 x}{x - 5} = 15$

$x = 5 \left(x - 5\right)$

$4 x = 25$

$x = \frac{25}{4}$

$x = 6.25$

3) Consider

$\setminus \frac{5 x - 30}{x - 5} = 15$

$5 x - 30 = 15 \left(x - 5\right)$

$10 x = 45$

$x = 4.5$

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