Question

Show that [x^-1 + y^-1]/[x+y]=(xy)^-1

Answer 1

Answer:

LHS=(1/x+1/y)/(x+y)

x+y/xy/x+y/1

1/xy

(xy)^-1

RHS=(xy)^-1

LHS=RHS

Hence proved

Step-by-step explanation:

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Answer 2

Answer:

[x^-1 + y^-1]/[x+y]=(xy)^-1

» [1/x+1/y]/[x+y]= 1/xy

» [y/xy + x/xy] / [x+y] = 1/xy

» [y+x]/xy/[x+y] = 1/xy

» [y+x] / [x²y+xy²] = 1/xy

» [y+x] / (xy) [x+y] = 1/xy

» 1/xy = 1/xy

» (xy)-¹ = (xy) -¹

hence proved