SOLUTION: I have been struggling with this equation for 3 days, and can not understand what I am doing wrong to see the appropriate way to approach solving these types of problems. Please he

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Question 109881This question is from textbook Algebra for college students
: I have been struggling with this equation for 3 days, and can not understand what I am doing wrong to see the appropriate way to approach solving these types of problems. Please help me understand how to approach solving these types of problems, and what to look for to determine the appropriate method to finding the solution?
{{z/Z+3}={3Z/5Z-1}}
This question is from textbook Algebra for college students

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Z%2F%28Z%2B3%29=+3Z%2F%285Z-1%29……. I guess you need Z%2B3 and 5Z-1 to be denominators; therefore, you need parenthesis ( )
It also might be that you need 5%28Z-1%29 instead of 5Z-1

If you need to write Z%2B3 and 5Z-1, then we will have:
Z%2F%28Z%2B3%29=+3Z%2F%285Z-1%29…….divide both sides by Z
1%2F%28Z%2B3%29=+3%2F%285Z-1%29…….move 3%2F%285Z-1%29 to the left
1%2F%28Z%2B3%29+-+3%2F%285Z-1%29+=+0…….now Least Common Denominator
%281%285Z-1%29+-+3+%28Z%2B3%29%29+%2F%285Z-1%29%28Z%2B3%29+=+0…….
%285Z-1+-+3+Z-9%29%29+%2F%285Z-1%29%28Z%2B3%29+=+0…….

%282Z+-10%29+%2F%285Z-1%29%28Z%2B3%29+=+0…….
%282%28Z+-+5%29%29+%2F%285Z-1%29%28Z%2B3%29+=+0…….
If you need to write Z%2B3 and 5%28Z-1%29, then we will have:
Z%2F%28Z%2B3%29=+3Z%2F5%28Z-1%29…….divide both sides by Z
1%2F%28Z%2B3%29=+3%2F5%28Z-1%29…….move 3%2F%285Z-1%29 to the left
1%2F%28Z%2B3%29+-+3%2F5%28Z-1%29+=+0…….now Least Common Denominator
%281%285Z-1%29+-+3+%28Z%2B3%29%29+%2F5%28Z-1%29%28Z%2B3%29+=+0…….
%285Z-1+-+3+Z-9%29%29+%2F5%28Z-1%29%28Z%2B3%29+=+0…….

%282Z+-10%29+%2F5%28Z-1%29%28Z%2B3%29+=+0…….
%282%28Z+-+5%29%29+%2F5%28Z-1%29%28Z%2B3%29+=+0…….