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Question

Solve for x:1(a+b+x)=1a+1b+1x,[a0,b0,x0,x(a+b)]

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Solution

Given, 1(a+b+x)=1a+1b+1x

1a+b+x=bx+ax+ababx

abx=(a+b+x)(ax+bx+ab)

abx=a2x+abx+a2b+abx+b2x+ab2+ax2+bx2+abx

0=2x[ab+a2+b2]+ab[a+b]

2x[ab+a2+b2]=ab[a+b]

x=ab[a+b]2[ab+a2+b2]

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