We need to solve the following equation:
[tex]\frac{5x}{x-1}+5=\frac{15}{x-1}[/tex]
Notice that x ≠ 1, since x = 1 makes zero the denominators. Then, multiplying all the terms by x-1, we obtain:
[tex]\begin{gathered} \frac{5x}{x-1}\cdot(x-1)+5(x-1)=\frac{15}{x-1}\cdot(x-1) \\ \\ 5x\cdot\frac{x-1}{x-1}+5x-5=15\cdot\frac{x-1}{x-1} \\ \\ 5x+5x-5=15 \\ \\ 10x-5=15 \\ \\ 10x-5+5=15+5 \\ \\ 10x=20 \\ \\ \frac{10x}{10}=\frac{20}{10} \\ \\ x=2 \end{gathered}[/tex]
