Simplify the expression: 2 - (y5)/(4)y(5)/(4) - y^(1)/(4)

The given expression is $2 - \frac{y^{\frac{5}{4}}}{y^{\frac{5}{4}} - y^{\frac{1}{4}}}$.
Let's first simplify the fraction $\frac{y^{\frac{5}{4}}}{y^{\frac{5}{4}} - y^{\frac{1}{4}}}$.
Factor out the term with the smallest exponent, $y^{\frac{1}{4}}$, from the denominator:

$$\frac{y^{\frac{5}{4}}}{y^{\frac{1}{4}}\left(y^{\frac{5}{4} - \frac{1}{4}} - 1\right)}$$ $$\frac{y^{\frac{5}{4}}}{y^{\frac{1}{4}}\left(y^{\frac{4}{4}} - 1\right)}$$ $$\frac{y^{\frac{5}{4}}}{y^{\frac{1}{4}}(y - 1)}$$

Now, use the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ to simplify the $y$ terms:

$$\frac{y^{\frac{5}{4} - \frac{1}{4}}}{y - 1}$$ $$\frac{y^{\frac{4}{4}}}{y - 1}$$ $$\frac{y}{y - 1}$$

The expression becomes:

$$2 - \frac{y}{y - 1}$$

The common denominator is $(y - 1)$.

$$\frac{2(y - 1)}{y - 1} - \frac{y}{y - 1}$$ $$\frac{2(y - 1) - y}{y - 1}$$ $$\frac{2y - 2 - y}{y - 1}$$ $$\frac{(2y - y) - 2}{y - 1}$$ $$\frac{y - 2}{y - 1}$$