a=ba=b
(step 1) Multiply both sides by bb:
ab=b2ab=b2
(step 2) Subtract a2a2 from both sides and factorize:
ab−a2=b2−a2ab−a2=b2−a2
(step 3)
a(b−a)=(b+a)(b−a)a(b−a)=(b+a)(b−a)
(step 4) Simplify and add 1 to both sides:
a=b+a
(step 5)
a+1=b+a+1a+1=b+a+1
Now since a=ba=b (the starting point of this proof), we can write this as:
a+1=2a+1a+1=2a+1
And in the case where a=1a=1, we have:
1+1=2+11+1=2+1
So, therefore,
1+1=3
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