document.write( "Question 635103: If X/(b+c-a) = Y/(c+a-b) = Z/(a+b-c) then (b-c)x + (c-a)y + (a-b)Z is? \n" ); document.write( "
Algebra.Com's Answer #400096 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( " =  = \r\n" );
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document.write( "Taking the first two fractions\r\n" );
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document.write( "Cross multiplying:\r\n" );
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document.write( "{x(c+a-b) = y(b+c-a)\r\n" );
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document.write( "x(-b+c+a) = y[b+(c-a)]\r\n" );
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document.write( "x[(-b+c)+a] = yb+y(c-a)\r\n" );
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document.write( "x[-(b-c)+a] = yb+y(c-a)\r\n" );
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document.write( "-x(b-c)+xa = yb+y(c-a)\r\n" );
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document.write( "xa-yb = x(b-c)+y(c-a)     <--- equation (1)\r\n" );
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document.write( "Taking the first and third fractions:\r\n" );
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document.write( "x(a+b-c) = z(b+c-a)\r\n" );
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document.write( "x[a+(b-c)] = z(-a+b+c)\r\n" );
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document.write( "xa+x(b-c) = z[(-a+b)+c]\r\n" );
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document.write( "xa+x(b-c) = z[-(a-b)+c]\r\n" );
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document.write( "xa+x(b-c) = -z(a-b)+zc\r\n" );
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document.write( "x(b-c)+z(a-b) = zc-xa     <--- equation (2)\r\n" );
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document.write( "Taking the second and third fractions:\r\n" );
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document.write( " = \r\n" );
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document.write( "Cross-multiplying:\r\n" );
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document.write( "y(a+b-c) = z(c+a-b)\r\n" );
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document.write( "y(-c+a+b) = z[c+(a-b)]\r\n" );
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document.write( "y[(-c+a)+b] = zc+z(a-b)\r\n" );
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document.write( "y[-(c-a)+b] = zc+z(a-b)\r\n" );
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document.write( "-y(c-a)+yb = zc+z(a-b)\r\n" );
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document.write( "yb-zc = y(c-a)+z(a-b)     <--- equation (3)\r\n" );
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document.write( "Putting equations (1), (2), and (3) together\r\n" );
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document.write( "xa-yb = x(b-c)+y(c-a)     <--- equation (1)\r\n" );
document.write( "x(b-c)+z(a+b) = zc-xa     <--- equation (2)\r\n" );
document.write( "yb-zc = y(c-a)+z(a-b)     <--- equation (3)\r\n" );
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document.write( "Reversing equation (2)\r\n" );
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document.write( "xa-yb = x(b-c)+y(c-a)     <--- equation (1)\r\n" );
document.write( "xc-xa = x(b-c)+z(a-b)     <--- equation (2)\r\n" );
document.write( "yb-zc = y(c-a)+z(a-b)     <--- equation (3)\r\n" );
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document.write( "Adding all three equation (equals added to equals give equals)\r\n" );
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document.write( "xc-zc =2x(b-c)+2y(c-a)+2z(a-b)\r\n" );
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document.write( "Dividing through by 2\r\n" );
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document.write( " = x(b-c)+y(c-a)+z(a-b)\r\n" );
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document.write( "or if you like:\r\n" );
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document.write( "(b-c)x+(c-a)y+(a-b)z = \r\n" );
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document.write( "Edwin
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