the rational expression in simplest

[spacewater]

3xy / xy + y

I am having a trouble figuring out this problem. I thought the xy on the denominator and numerator cancel out each other and becomes 3/y but I was wrong. Can someone show me a proper steps to solving this problem? Thanks

 

[Loren]

You need to use grouping symbols to clarify what you mean. Using the order of operations in their strictest sense...

3xy / xy + y means $\displaystyle \frac{3xy}{x}y+y$.

3xy / (xy) + y means $\displaystyle \frac{3xy}{xy}+y$.

3xy / (xy + y) means $\displaystyle \frac{3xy}{xy+y}$.

 

[galactus]

Please try to use proper grouping symbols.

If this is correct, they do not cancel because there is a sum in the denominator. If it were $\displaystyle \frac{3xy+y}{xy}$, then you could do that.

$\displaystyle \frac{3xy}{xy+y}=\frac{3x\rlap{/}y}{\rlap{/}y(x+1)}=\frac{3x}{x+1}$