Question #55694

1 Answer
Ken C.
Aug 22, 2016

They combined the like terms.

Explanation:

Let's begin at #16/9y^2+y^2=25#. We can see that both terms on the left have a #y^2#:
#16/9color(red)(y^2)+color(red)(y^2)=25#

Recall from algebra that we can combine these like terms. It's the same idea as this:
#x+x+x=9#
#3x=9->x=3#

You can add the three #x#s together to get #3x#. In your example, we're going to add the #16/9y^2# and the #y^2# together:
#16/9y^2+y^2=25#
#(16y^2)/9+(9y^2)/9=25# (#16/9y^2# and #(16y^2)/9# are the same thing)
#(25y^2)/9=25# or #25/9y^2=25#

As you can see, we just added the fractions.

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