solve 1/(a+b+x)=1/a+1/b+1/x a+bnot=0
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1/(a+b+x)=1/a+1/b+1/x1/(a+b+x) - 1/x=1/a+1/b
(x - a - b - x)/x(a+b + x) = (a + b )/ab
Let a+ b + x = k
-1(a+b)/x(a + b + x) = a + b/ab
-1/x(a + b + x) =1/ab
x(a + b + x) = -ab
ax + bx + x^2 + ab = 0
[tex]x^2 + ax + bx + ab = 0 x^2 - (-a -b)x + ab = 0 \alpha + \beta = -a-b \alpha \beta = ab \alpha = -a \beta = -b [/tex]
Therefore x = -a,-b
(x - a - b - x)/x(a+b + x) = (a + b )/ab
Let a+ b + x = k
-1(a+b)/x(a + b + x) = a + b/ab
-1/x(a + b + x) =1/ab
x(a + b + x) = -ab
ax + bx + x^2 + ab = 0
[tex]x^2 + ax + bx + ab = 0 x^2 - (-a -b)x + ab = 0 \alpha + \beta = -a-b \alpha \beta = ab \alpha = -a \beta = -b [/tex]
Therefore x = -a,-b
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