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Question

Simplify the equation: 1a+b+x=1a+1b+1x;a+b0

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Solution

1a+b+x=1a+1b+1x a+b0
=1a+b+x=bx+ax+ababx
=abx=(a+b+x)(bx+ax+ab)
abx=(a+b)2x+(a+b)ab+x2(a+b)+abx
(a+b)2x+(a+b)x2+a2b+ab2=0
(a+b)x2+(a+b)2+(a+b)ab=0
x2+(a+b)x+ab=0
x=(a+b)±(a+b)24ab2=(a+b)±(ab)2
x=ab+ab2,x=aba+b2
x=b x=a
x=a,b

1086895_1166955_ans_4e9a9260142b476c84cf3cc086aa6270.png

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