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Sagot :

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}.

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