Question 927055
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            The analysis in the post by  @CubeyThePenguin  is incomplete;


            the answer is incomplete,  too.



<pre>
You start from


    {{{a/b}}} + {{{(a + 10b)/(b + 10a)}}} = 2.


You introduce new variable  x = {{{a/b}}}  (which is under the problem's question).


Then you divide the numerator and the denominator in the given equation by "b".

You will get then this equation for x


    x + {{{(x+10)/(1 + 10x)}}} = 2.


By multiplying both sides by (1+10x), you get

    x*(1+10x) + (x+10) = 2*(1+10x)

    x + 10x^2 + x + 10 = 2 + 20x

    10x^2 - 18x + 8 = 0


Using the quadratic formula, you get 2 (two, TWO)  roots for x

    {{{x[1]}}} = 1  and  {{{x[2]}}} = {{{4/5}}}.


<U>ANSWER</U>.  There are 2 (two, TWO) solutions  {{{a/b}}} = 1  and  {{{a/b}}} = {{{4/5}}}.
</pre>

Solved (correctly).



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Hello,  &nbsp;@CubeyThePenguin, &nbsp;consider to hire somebody, &nbsp;who will assist you by editing / fixing your solutions after you.