X2 +5x+6 / x2+4x+4 = 3x+1 / 5x-2 ;x is not equal to -2 ,2/5

Asked by M.s.srinidhi21 | 30th Sep, 2014, 08:45: AM

Expert Answer:

fraction numerator x squared plus 5 x plus 6 over denominator x squared plus 4 x plus 4 end fraction equals fraction numerator 3 x plus 1 over denominator 5 x minus 2 end fraction rightwards double arrow fraction numerator x squared plus 3 x plus 2 x plus 6 over denominator left parenthesis x plus 2 right parenthesis squared end fraction equals fraction numerator 3 x plus 1 over denominator 5 x minus 2 end fraction rightwards double arrow fraction numerator x left parenthesis x plus 3 right parenthesis plus 2 left parenthesis x plus 3 right parenthesis over denominator left parenthesis x plus 2 right parenthesis squared end fraction equals fraction numerator 3 x plus 1 over denominator 5 x minus 2 end fraction rightwards double arrow fraction numerator left parenthesis x plus 2 right parenthesis left parenthesis x plus 3 right parenthesis over denominator left parenthesis x plus 2 right parenthesis squared end fraction equals fraction numerator 3 x plus 1 over denominator 5 x minus 2 end fraction rightwards double arrow fraction numerator x plus 3 over denominator x plus 2 end fraction equals fraction numerator 3 x plus 1 over denominator 5 x minus 2 end fraction left square bracket because x not equal to minus 2 right square bracket rightwards double arrow left parenthesis x plus 3 right parenthesis left parenthesis 5 x minus 2 right parenthesis equals left parenthesis x plus 2 right parenthesis left parenthesis 3 x plus 1 right parenthesis rightwards double arrow 5 x squared minus 2 x plus 15 x minus 6 equals 3 x squared plus x plus 6 x plus 2 rightwards double arrow 2 x squared plus 6 x minus 8 equals 0 rightwards double arrow x squared plus 3 x minus 4 equals 0 rightwards double arrow x squared plus 4 x minus x minus 4 equals 0 rightwards double arrow x left parenthesis x plus 4 right parenthesis minus 1 left parenthesis x plus 4 right parenthesis equals 0 rightwards double arrow left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis equals 0 therefore x equals 1 comma minus 4

Answered by Prasenjit Paul | 30th Sep, 2014, 10:34: AM

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