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Question

Solve the following equations:
x+12axx12ax=a+1a1.

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Solution

x+12axx+12ax=a+1a1
Applying Componendo and Dividendo
x12ax=a1
Squaring both sides
x212ax=ax2=12a2axx2+ax12a2=0x2+4ax3ax12a2=0x(x+4a)3a(x+4a)=0(x3a)(x+4a)=0x=4a,3a

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(x + a)(x +b)= x^2 + x(a+ b) + ab
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