Đáp án + Giải thích các bước giải:

`45/(x+3)+45/(x-3)=25/4(ĐKXĐ:x\ne+-3)`

`<=>(45(x-3))/((x+3)(x-3))+(45(x+3))/((x-3)(x+3))=25/4`

`<=>(45x-135)/((x+3)(x-3))+(45x+135)/((x-3)(x+3))=25/4`

`<=>(45x-135+45x+135)/((x+3)(x-3))=25/4`

`<=>(90x)/((x+3)(x-3))=25/4`

`=>90x.4=25(x+3)(x-3)`

`<=>360x=25(x^2-9)`

`<=>360x=25x^2-225`

`<=>25x^2-360x-225=0`

`<=>5(5x^2-72x-45)=0`

`<=>5x^2-72x-45=0`

`<=>5x^2-75x+3x-45=0`

`<=>(5x^2-75x)+(3x-45)=0`

`<=>5x(x-15)+3(x-15)=`0

`<=>(5x+3)(x-15)=0`

`<=>` \(\left[ \begin{array}{l}5x+3=0\\x-15=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}5x=-3\\x=15\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=-\dfrac{3}{5}(tmđk)\\x=15(tmđk)\end{array} \right.\) 

Vậy phương trình có nghiệm `S={-3/5;15}`