Algebra Question...Not quite sure what to do

How do I solve the following:

Solve for y

5 + 3y/y + 19 + y/y = 100

I bet you mean (5 + 3y)/y + (19 + y)/y = 100 else the y’s cancel.

Multiply both sides by y to get

(5 + 3y) + (19 + y) = 100y

24 + 4y = 100y
24 = 94y, so y = 24/96 = 1/4

Check this result in the original equation, I did!

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I've seen this error so often that I have created a boilerplate:

When writing a division using two lines (as on a sheet of paper) there is a line to separate the two numbers and indicate it is division. That line is called the “vinculum,” a word derived from Latin.

2
-- → Is called the “vinculum” and means 2 ÷ 3, read “2 divided by 3.”
3

When writing this expression on one line only, use “/” as the division sign: 2/3. This symbol became needed when computers could not understand two line division symbols and “÷” is not on the standard keyboard. Since the “/” is on one line it is not a grouping symbol, so other grouping symbols are needed.

2 + 3×7
--------- When written on one line is (2 + 3×7)/(31 – 12); the parentheses are necessary!
31 ‒ 12

multiply 5 by y to get a common denominator
5y +3y+19+y = 100
-------------------
y
9y+19 = 100
--------
y
multiply both sides by y to remove y from denominator
9y+19 = 100 y

subtract 100 y from both sides
-81y +19 = 0
-19 -19
-81y=-19
-------------
-81 -81

y= 81/19

No solution.

The y's all cancel out.