What is this math expression equivalent to?

Question

Hello, Im having difficulties with this problem....

1/3+1/3x
--------------------------
1/x+1/3


the answers are

x+1/ x+3

2

3x+3/x+3

1/3

Please help. Thanks. Also if you can explain how to get the answer. I would appreciate it.

Answer 1

common denominator of all 4 of the fractions is 3x, so multiply each one by 3x, which will cancel with each denominator in some way

3x(1/3) + (3x)(1/3x)
-------------------------
3x(1/x) + 3x(1/3)


x + 1
---------
3 + x

Your first answer choice is the correct one

Answer 2

Start out by creating common denominators
for the two expressions.

1/3 + 1/3x = 1/3 * x/x + 1/3x = x/3x + 1/3x = (x+1)/3x

1/x + 1/3 = 1/x * 3/3 + 1/3 * x/x = 3/3x + x/3x = (x+3)/3x

so the original problem turns into

(x+1)/3x
----------
(x+3)/3x

When you divide by a fraction, you can flip the fraction
over and multiply:

(x+1)/3x * (3x/(x+3)

The 3x terms cancel out so you have

(x+1)/(x+3)

Answer 3

first, multiply by 3x/3x

x/1+1/1
-------------
3/1+x/1

=

(x+1)/1
_____
(3+x)/1

=

(x+1)
_____
(3+x)

Which simplifies to the same as your first possible answer