How many possible values can this have?

[mathsfreak]

Find all positive integers a and b such that

4/ab + 2/a + 1/b = 1

I cannot find a system that can ensure that I have all values.

Thanks for your help,

mathsfreak

 

[lookagain]

Find all positive integers a and b such that

4/ab + 2/a + 1/b = 1

You need grouping symbols:

4/(ab) + 2/a + 1/b = 1

Suggestions:

Multiply all four quantities by ab.

Get the terms involving a on one side of an equation and
terms not involving a on the opposite side. Factor the a
variable out.

Solve for a. You would have a is equal to a fraction
involving b and constants.

Try long division on the algebraic fraction involving
b to find allowable b-values and allowable a-values.

 

[pka]

Find all positive integers a and b such that
4/ab + 2/a + 1/b = 1

Multiply by \(ab\).
\(4+2b+a=ab\\2b+4=ab-a\\2(b+2)=a(b-1)\)
Can you try various values?