| Consider two positive numbers \(a\) and \(b\) that are equal: | $$ a = b $$ |
| Multiply both sides of this equation by \(a\), | $$ a^{2}=ab $$ |
| Subtract \(b^2\) from both sides. | $$ a^{2}-b^{2}=ab-b^{2} $$ |
| Factorise both sides | $$ (a-b)(a+b)=b(a-b) $$ |
| Divide both sides by \( (a - b) \). | $$a+b=b $$ |
| As \( a = b \) substitute \(b\) for \(a\). | $$ b+b=b $$ |
| Collect like terms | $$ 2b=b $$ |
| Divide both sides by \( b \). | $$2 = 1 $$ |
| How can this be? | $$???$$ |
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