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[" 6."(1)/(2)quad (1)/(3)quad (1)/(3(x-y...

[" 6."(1)/(2)quad (1)/(3)quad (1)/(3(x-y))=0;x+y!=0,x-y!=0],[(6)/(x+y)-(7)/(x-y)=3,((1)/(2(x+y))-(1)/(2(x+y)))/(15)]

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(6)/(x+y)=(7)/(x-y)+3(1)/(2(x+y))=(1)/(3(x-y))

6/(x+y)=7/(x-y)+3 , 1/(2(x+y))=1/(3(x-y))

Solve for x and y (2)/(x)+(2)/(3y)=(1)/(6),(3)/(x)+(2)/(y)=0

( 1 ) /(x) + (1 ) /( y) = 7 , ( 2)/(x) + ( 3) /( y) = 17 (x ne 0, y ne 0 ) .

Solve:(1)/(2(2x+3y))+(12)/(7(3x-2y))=(1)/(2)(7)/(2x+3y)+(4)/(3x-2y)=2 where 2x+3y!=0 and 3x-2y!=0

A triangle has vertices A_(i) (x_(i),y_(i)) for i= 1,2,3,. If the orthocenter of triangle is (0,0) then prove that |{:(x_(2)-x_(3),,y_(2)-y_(3),,y_(1)(y_(2)-y_(3))+x_(1)(x_(2)-x_(3))),(x_(3)-x_(1) ,,y_(3)-y_(1),,y_(2)(y_(3)-y_(1))+x_(2)(x_(3)-x_(1))),( x_(1)-x_(2),,y_(1)-y_(2),,y_(3)(y_(1)-y_(2))+x_(3)(x_(1)-x_(2))):}|=0

A triangle has vertices A_(i) (x_(i),y_(i)) for i= 1,2,3,. If the orthocenter of triangle is (0,0) then prove that |{:(x_(2)-x_(3),,y_(2)-y_(3),,y_(1)(y_(2)-y_(3))+x_(1)(x_(2)-x_(3))),(x_(3)-x_(1) ,,y_(3)-y_(1),,y_(2)(y_(3)-y_(1))+x_(2)(x_(3)-x_(1))),( x_(1)-x_(2),,y_(1)-y_(2),,y_(3)(y_(1)-y_(2))+x_(3)(x_(1)-x_(2))):}|=0

A triangle has vertices A_(i) (x_(i),y_(i)) for i= 1,2,3,. If the orthocenter of triangle is (0,0) then prove that |{:(x_(2)-x_(3),,y_(2)-y_(3),,y_(1)(y_(2)-y_(3))+x_(1)(x_(2)-x_(3))),(x_(3)-x_(1) ,,y_(3)-y_(1),,y_(2)(y_(3)-y_(1))+x_(2)(x_(3)-x_(1))),( x_(1)-x_(2),,y_(1)-y_(2),,y_(3)(y_(1)-y_(2))+x_(3)(x_(1)-x_(2))):}|=0