# How do I rewrite this expression into another specific expression

Hi so I've got this problem for university and I just can't see how I'm supposed to rewrite this expression: $$\dfrac{\exp(\mathbf{w^{t}x} + w_{0})}{\exp{(\mathbf{w^{t}x}} + w_{0}) + 1}$$ into this: $$\dfrac{1}{1 + \exp(-a)}$$ where $$\textit{a}$$ can be any value.

I first tried simplifying the expression which lead to: $$1 - \dfrac{1}{1 + \exp(\mathbf{w^tx} + w_{0})}$$, this almost looks like what is required, $$\textit{a}$$ would then obviously be: $$-\mathbf{w^{t}x} + w_{0}$$. But I don't really know how to get rid of the 1 at the beginning of the resulting expression, nor do I see how I could otherwise rewrite/simplify it.

Any help is appreciated.

• Divide both the numerator and the denominator by $$\exp(w^Tx + w_0)$$