Question 114543
{{{((x-a)/(b+c))+((x-b)/(c+a))+((x-c)/(a+b))=3}}}………… common denominator {{{ ((b+c)( c+a)( a+b)) }}}

{{{(((x-a)( c+a)( a+b) +(x-b)(b+c)( a+b) + (x-c)(b+c)(c+a)) /(b+c)( c+a)( a+b))=3}}}………… ......multiply both sides by common denominator



{{{ (x-a)( c+a)( a+b)  +  (x-b)(b+c)( a+b)  +  (x-c)(b+c)( c+a)= 3(b+c)( c+a)( a+b)  }}}………..………..multiply 

{{{ (cx + ax-ac - a^2)( a+b) + (bx +cx-b^2-bc)( a+b)  + (bx+cx-bc-c^2)( c+a)= 3((bc+ab+c^2+ac)( a+b))  }}}........multiply
	
{{{ (acx + bcx + a^2x +abx-a^2c - acb-a^3-a^2b) + (abx +acx-ab^2-abc+b^x+bcx-b^3-b^c) + (bcx+c^2x-bc^2-c^3+abx+acx-abc-ac^2)= 3((abc+a^2b+ac^2+a^2c +b^2c+ab^2+bc^2+abc))  }}}........

{{{ acx + bcx + a^2x +abx-a^2c - acb-a^3-a^2b + abx +acx-ab^2-abc+b^x+bcx-b^3-b^c + bcx+c^2x-bc^2-c^3+abx+acx-abc-ac^2= 3((abc+a^2b+ac^2+a^2c +b^2c+ab^2+bc^2+abc))  }}}........

{{{ 3acx + 3bcx + a^2x + 3abx - a^2c - 3abc - a^3 - a^2b - ab^2 + b^2x - b^3 - b^2c + c^2x - bc^2 - c^3 - ac^2= 3(abc+a^2b+ac^2+a^2c +b^2c+ab^2+bc^2+abc)  }}}........


{{{ - a^3 - b^3 - c^3 + 3acx + 3bcx + a^2x + 3abx - a^2c - 3abc  - a^2b - ab^2 + b^2x - b^2c + c^2x - bc^2  - ac^2= 6abc+ 3a^2b +3ac^2+ 3a^2c + 3b^2c + 3ab^2+ 3bc^2}}}........move all terms from the right to the left

{{{ - a^3 - b^3 - c^3 + 3acx + 3bcx + a^2x + 3abx - a^2c - 3abc  - a^2b - ab^2 + b^2x - b^2c + c^2x - bc^2  - ac^2-6abc-3a^2b - 3ac^2- 3a^2c - 3b^2c - 3ab^2- 3bc^2 = 0}}}........


{{{ - a^3 - b^3 - c^3 + 3acx + 3bcx + 3abx + a^2x  + b^2x + c^2x -9abc - 4a^2b - 4ac^2- 4a^2c - 4b^2c - 4ab^2- 4bc^2 = 0}}}........

{{{ - a^3 - b^3 - c^3 + 3x(ac + bc + ab) + x(a^2  + b^2 + c^2) -9abc - 4a(ab - ac^2- ac) - 4b(bc - ab- bc^2) = 0}}}........

{{{ - a^3 - b^3 - c^3  + x(a^2  + b^2 + c^2) + 3x(ac + bc + ab) - 4a(ab - ac^2- ac) - 4b(bc - ab- bc^2)-9abc  = 0}}}........