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- anonymous

2y+3/y = 3/2 rational expression help

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- anonymous

2y+3/y = 3/2 rational expression help

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- anonymous

- freckles

are you trying to solve an equation?

- freckles

\[2y+\frac{3}{y}=\frac{3}{2} \\ \text{ multiply both sides by } y \neq 0 \\ y(2y+\frac{3}{y})=y(\frac{3}{2} )\\ y(2y)+y(\frac{3}{y})=\frac{3}{2}y \\ 2y^2+3=\frac{3}{2} y \\ \text{ if you don't want \to deal with any fractions multiply both sides by 2 } \\ 4y^2+6=3y \\ \text{ subtract} 3y \text{ on both sides } 4y^2-3y+6=0\]
you have a quadratic equation to solve.
but the equation you wrote is probably not the equation you meant
you probably meant
\[\frac{2y+3}{y}=\frac{3}{2}\]
though I could be wrong about that too
you did say rational expression after all and you have an equation composed of rational expressions on left and right side

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- freckles

and if you meant the last equation I wrote which
is (2y+3)/y=3/2
I would still multiply both sides by y and 2

- freckles

\[2(2y+3)=3(y) \\ 4y+6=3y \]

- anonymous

@freckles than what

- freckles

you solve for y

- freckles

And I still don't know what equation you mean

- anonymous

@freckles The second equation you showed

- freckles

ok do something to get your y terms on one side

- anonymous

@freckles Thanks

- freckles

what did you get?

- freckles

\[2(2y+3)=3(y) \\ 4y+6=3y\]
You subtracted 4y on both sides right?

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