1/a+b+x=1/a +1/b +1/x

Asked by jayjrd | 27th Jan, 2017, 06:49: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n : 1 over a plus 1 over b plus 1 over x equals fraction numerator 1 over denominator a plus b plus x end fraction comma space a comma b comma x not equal to 0 rightwards double arrow fraction numerator b x plus a x plus a b over denominator a b x end fraction equals fraction numerator 1 over denominator a plus b plus x end fraction rightwards double arrow open parentheses b x plus a x plus a b close parentheses open parentheses a plus b plus x close parentheses equals a b x rightwards double arrow a b x plus b squared x plus b x squared plus a squared x plus a b x plus a x squared plus a squared b plus a b squared plus a b x equals a b x rightwards double arrow open parentheses a plus b close parentheses x squared plus a squared x plus 2 a b x plus plus b squared x plus a squared b plus a b squared equals 0 rightwards double arrow open parentheses a plus b close parentheses x squared plus open parentheses a plus b close parentheses squared x plus a squared b plus a b squared equals 0 rightwards double arrow open parentheses a plus b close parentheses x squared plus open parentheses a plus b close parentheses squared x plus a b open parentheses a plus b close parentheses equals 0 D i v i d e space t h e space a b o v e space e q u a t i o n space b y space a plus b comma space w e space h a v e comma x squared plus open parentheses a plus b close parentheses x plus a b equals 0 S o l v i n g space t h e space a b o v e space q u a d r a t i c comma space w e space h a v e comma x equals fraction numerator minus open parentheses a plus b close parentheses plus-or-minus square root of open parentheses a plus b close parentheses squared minus 4 a b end root over denominator 2 end fraction rightwards double arrow x equals fraction numerator minus open parentheses a plus b close parentheses plus-or-minus square root of a squared plus 2 a b plus b squared minus 4 a b end root over denominator 2 end fraction rightwards double arrow x equals fraction numerator minus open parentheses a plus b close parentheses plus-or-minus square root of a squared minus 2 a b plus b squared end root over denominator 2 end fraction rightwards double arrow x equals fraction numerator minus open parentheses a plus b close parentheses plus-or-minus square root of open parentheses a minus b close parentheses squared end root over denominator 2 end fraction rightwards double arrow x equals fraction numerator minus open parentheses a plus b close parentheses plus-or-minus open parentheses a minus b close parentheses over denominator 2 end fraction rightwards double arrow x equals minus a comma space x equals minus b

Answered by Rebecca Fernandes | 29th Jan, 2017, 09:22: AM