.
First part of my answer.
If it is
=
then, after multiplying both sides by x*(x+1), you have
20*(x+1) + 20*x = 9x*(x+1) ====> 20x + 20 + 20x = 9x^2 + 9x ====>
9x^2 - 31x - 20 = 0 ====> after factoring the left side ====>
(9x+5)*(x-4) = 0 ====> the solutions are x = and x = 4.
Second part of my answer
Your formula is ambiguous and unreadable without using parentheses.
Is it (1/x) + (1/x) + 1 = (9/20) or (1/x) + (1/(x+1)) = 9/20 ??
Use parentheses to make your formulas readable and unambiguous.
Use parentheses when you post your formulas to this forum.
It is the REQUIREMENT of this site.
There is NO OTHER WAY to make them readable and unambiguous.
By violating this RULE, you work against yourself and against your better interests.
With it, welcome to the forum !!
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I repeat this mantra to each and every new visitor coming to this forum,
until he or she will take it seriously.
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Once, when I sent this message to some customer/"student"/visitor, he responded me (through the "Thank you" form),
asking why he (or she ?) should use parentheses when his source (textbook, teacher's assignment sheet and so on)
does not contain these parentheses ?
Good question !
The answer is: That sources have TYPOGRAPHY MEANS to represent the fractions, writing them in two levels /
numerators and denominators, divided by horizontal lines.
Such typography tools ABSENT in this forum, THEREFORE the customers SHOULD write parentheses to present numerators and denominators
explicitly.
Hope this explanation makes this issue absolutely clear.