We have the next equation
[tex]\frac{5}{3x-2}=\frac{2}{x+1}[/tex]
First, we will multiplicate x+1 on both sides
[tex]\frac{5(x+1)}{(3x-2)}=\frac{2(x+1)}{x+1}[/tex][tex]\frac{5(x+1)}{(3x-2)}=2[/tex]
then we multiply 3x-2 on both sides
[tex]\frac{5(x+1)(3x-2)}{(3x-2)}=2(3x-2)[/tex]
[tex]5(x+1)=2(3x-2)[/tex]
then we do the products
[tex]5x+5=6x-4[/tex]
then we sum like terms
[tex]\begin{gathered} 5x-6x=-5-4 \\ \end{gathered}[/tex][tex]-x=-9[/tex]
therefore
[tex]x=9[/tex]
The solution set is {9}.
