Algebra.Com's Answer #839347 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "Find A, B and C if  +  +  = 
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document.write( "They want you find A, B, C from this given identity\r\n" );
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document.write( " + + = \r\n" );
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document.write( "This problem is, in some sense, a joking and entertainment Math problem.\r\n" );
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document.write( "Indeed, there are different ways/methods to solve it.\r\n" );
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document.write( "One way, shown by the other tutor, is direct and straightforward, but requires a lot of computations,\r\n" );
document.write( "such as reducing the problem to a system of 3 linear equations and solving this system.\r\n" );
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document.write( "This way is like a torture and can only bring tears.\r\n" );
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document.write( "But there are other ways, so beautiful that you will smile learning them.\r\n" );
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document.write( "One of such method is my solution under this link\r\n" );
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document.write( "https://www.algebra.com/algebra/homework/expressions/expressions.faq.question.1196220.html\r\n" );
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document.write( " | The other method I will show right here. |\r\n" );
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document.write( "Multiply the given identity by (x-1). Then from the given identity (1), you will get this identity\r\n" );
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document.write( " A +  +  =  . (2)\r\n" );
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document.write( "In this identity, place x= 1. In its left side, you will get the second and the third addends zeroed\r\n" );
document.write( "due to presence of the factor (x-1) in the numerator. Right side of (2) at x= 1 is\r\n" );
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document.write( "  =  =  = 1.\r\n" );
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document.write( "Thus A = 1.\r\n" );
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document.write( "Let's find B in similar way. Multiply the given identity by (x-2). Then from the given identity (1), \r\n" );
document.write( "you will get this identity\r\n" );
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document.write( "  + B +  =  . (3)\r\n" );
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document.write( "In this identity, place x= 2. In its left side, you will get the first and the third addends zeroed\r\n" );
document.write( "due to presence of the factor (x-2) in the numerator. Right side of (3) at x= 2 is\r\n" );
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document.write( "  =  =  = -2.\r\n" );
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document.write( "Thus B = -2.\r\n" );
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document.write( "Find C in similar way. Multiply the given identity by (x-3). Then from the given identity (1), \r\n" );
document.write( "you will get this identity\r\n" );
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document.write( "  +  + C =  . (4)\r\n" );
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document.write( "In this identity, place x= 3. In its left side, you will get the first and the second addends zeroed\r\n" );
document.write( "due to presence of the factor (x-3) in the numerator. Right side of (4) at x= 3 is\r\n" );
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document.write( "  =  =  = 3.\r\n" );
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document.write( "Thus C = 3.\r\n" );
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document.write( "ANSWER. A = 1, B = -2, C = 3.\r\n" );
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document.write( "Solved as a joke Math problem.\r
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document.write( "Next time, if you are given a similar functional identity of 10 addends with 10 unknown literal coefficients,
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document.write( "you do not need to reduce it to the system of 10 equations; you also do not need solve this system.\r
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document.write( "Simply apply this method and find the coefficients one after another, independently one from another,\r
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document.write( "spending one line for each coefficient.\r
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