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.

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