Answer:[tex]\frac{3y+2}{6y^2}[/tex]
Step-by-step explanation: Given rational expression : [tex]\frac{\frac{3y+2}{3y} }{\frac{6y^2+4y}{3y+2} }[/tex].
Rewriting it in proper form.
[tex]\frac{3y+2}{3y}[/tex] ÷[tex]\frac{6y^2+4y}{3y+2}[/tex]
Converting division sign into multiplication and flipping second fraction, we get
[tex]\frac{3y+2}{3y}[/tex]×[tex]\frac{3y+2}{6y^2+4y}[/tex]
Factoring out 2y from[tex]6y^2+4y[/tex]
[tex]6y^2+4y = 2y(3y+2)[/tex]
[tex]\frac{3y+2}{3y}[/tex]×[tex]\frac{3y+2}{2y(3y+2)}[/tex]
Crossing out common factors (3y+2) in second fraction, we get
=[tex]\frac{3y+2}{3y}[/tex]×[tex]\frac{1}{2y}[/tex]
=[tex]\frac{3y+2}{6y^2}[/tex].
