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 fraction numerator 1 over denominator 2 a plus b plus 2 x end fraction equals fraction numerator 1 over denominator 2 a end fraction plus 1 over b plus fraction numerator 1 over denominator 2 x end fractionsolve for x

Asked by Sanmit Ratnaparkhi 6th March 2015, 10:04 PM
Answered by Expert
Answer:
fraction numerator 1 over denominator 2 a plus b plus 2 x end fraction minus fraction numerator 1 over denominator 2 x end fraction equals fraction numerator 1 over denominator 2 a end fraction plus 1 over b rightwards double arrow fraction numerator negative left parenthesis 2 a plus b right parenthesis over denominator left parenthesis 2 a plus b plus 2 x right parenthesis 2 x end fraction equals fraction numerator 2 a plus b over denominator 2 a b end fraction rightwards double arrow fraction numerator negative 1 over denominator left parenthesis 2 a plus b plus 2 x right parenthesis 2 x end fraction equals fraction numerator 1 over denominator 2 a b end fraction rightwards double arrow left parenthesis 2 a plus b plus 2 x right parenthesis 2 x equals negative 2 a b rightwards double arrow left parenthesis 2 a plus b plus 2 x right parenthesis x equals negative a b rightwards double arrow 2 x squared plus x left parenthesis 2 a plus b right parenthesis plus a b equals 0 rightwards double arrow x equals fraction numerator negative left parenthesis 2 a plus b right parenthesis plus-or-minus square root of left parenthesis 2 a plus b right parenthesis squared minus 4 cross times 2 cross times a b end root over denominator 4 end fraction rightwards double arrow x equals fraction numerator negative left parenthesis 2 a plus b right parenthesis plus-or-minus square root of 4 a squared plus 4 a b plus b squared minus 8 a b end root over denominator 4 end fraction rightwards double arrow x equals fraction numerator negative left parenthesis 2 a plus b right parenthesis plus-or-minus square root of 4 a squared minus 4 a b plus b squared end root over denominator 4 end fraction rightwards double arrow x equals fraction numerator negative left parenthesis 2 a plus b right parenthesis plus-or-minus square root of left parenthesis 2 a minus b right parenthesis squared end root over denominator 4 end fraction rightwards double arrow x equals fraction numerator negative left parenthesis 2 a plus b right parenthesis plus-or-minus left parenthesis 2 a minus b right parenthesis over denominator 4 end fraction x equals fraction numerator negative 2 a minus b plus 2 a minus b over denominator 4 end fraction comma space x equals fraction numerator negative 2 a minus b minus 2 a plus b over denominator 4 end fraction x equals fraction numerator negative 2 b over denominator 4 end fraction comma space x equals fraction numerator negative 4 a over denominator 4 end fraction therefore x equals negative b over 2 comma negative a
Answered by Expert 7th March 2015, 9:57 AM
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