Simplify the expression 2 - (y1)/(3)y(1)/(4) - y^(1)/(3)

The given expression is $2 - \frac{y^{\frac{1}{3}}}{y^{\frac{1}{4}} - y^{\frac{1}{3}}}$.
Let's focus on the fraction $\frac{y^{\frac{1}{3}}}{y^{\frac{1}{4}} - y^{\frac{1}{3}}}$.
To simplify the exponents, find the least common multiple of the denominators of the fractions $\frac{1}{3}$ and $\frac{1}{4}$, which is 12.
Let $u = y^{\frac{1}{12}}$.
Then $y^{\frac{1}{3}} = y^{\frac{4}{12}} = (y^{\frac{1}{12}})^4 = u^4$.
And $y^{\frac{1}{4}} = y^{\frac{3}{12}} = (y^{\frac{1}{12}})^3 = u^3$.

Substitute these into the fraction:

$$\frac{u^4}{u^3 - u^4}$$

Factor out $u^3$ from the denominator:

$$\frac{u^4}{u^3(1 - u)}$$

Cancel $u^3$ from the numerator and denominator:

$$\frac{u}{1 - u}$$

The expression now becomes:

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

The common denominator is $1 - u$.

$$\frac{2(1 - u)}{1 - u} - \frac{u}{1 - u}$$ $$\frac{2 - 2u - u}{1 - u}$$ $$\frac{2 - 3u}{1 - u}$$