, 2026

Multiplying both sides of the equation by $2 \cdot 3 = 6$, we obtain $6 \cdot \dfrac{2t}{3} + 6\cdot\dfrac{3t}{2} = 6 \cdot 26$ or $4t + 9t = 156$.

Simplifying, we obtain $13t = 156$
and so $t = 12$.

Alternatively, using a common denominator of $2 \cdot 3 = 6$, we obtain $\dfrac{2 \cdot 2t}{2 \cdot 3} + \dfrac{3 \cdot 3t}{3 \cdot 2} = 26$ or $\dfrac{4t}{6} + \dfrac{9t}{6} = 26$.

Simplifying, we obtain $\dfrac{13t}{6} = 26$ and so $13t = 6 \cdot 26$
or $t = 6 \cdot 2 = 12$.
Multiplying both sides of the equation by $8$, we obtain $\dfrac{8(3+x)}{4} = 6 + x$ which
simplifies to $2(3+x) = 6 + x$.

Simplifying further, we obtain $6 + 2x = 6 + x$ and so $x = 0$.

Alternatively, splitting each fraction into two pieces, we obtain
$\dfrac{3}{4} + \dfrac{x}{4} = \dfrac{6}{8} + \dfrac{x}{8}$.

Since $\dfrac{3}{4} = \dfrac{6}{8}$,
we obtain $\dfrac{x}{4} = \dfrac{x}{8}$ and so $8x = 4x$ or $x = 0$.
Since $\text{y gt; 0}$, then $\sqrt{y^2} = y$.

From the given equation, we obtain $\sqrt{9 + 16 + 144} = \sqrt{9 + 16} + y$.

Thus, $\sqrt{169} = \sqrt{25} + y$ or
$13 = 5 + y$ and so $y = 8$.