Simplify the following: 3a+5b/4 + 9+b/8 2x/6 + 2x-3y/3 + x+y/2 (2a+4b)/4 - 3(a-4b)/6 3e+e2/4 + e2/3 5+4/8 - 25-2/4

Here are the solutions to the problems:

1. Simplify $\frac{3a+5b}{4} + \frac{9a+b}{8}$

Step 1: Find a common denominator for 4 and 8, which is 8. $\frac{3a+5b}{4} + \frac{9a+b}{8} = \frac{2(3a+5b)}{8} + \frac{9a+b}{8}$

Step 2: Add the numerators and combine like terms. $= \frac{6a+10b+9a+b}{8} = \frac{15a+11b}{8}$ The simplified expression is $\boxed{\frac{15a+11b}{8}}$.

2. Simplify $\frac{2x}{6} + \frac{2x-3y}{3} + \frac{x+y}{2}$

Step 1: Find a common denominator for 6, 3, and 2, which is 6. $\frac{2x}{6} + \frac{2x-3y}{3} + \frac{x+y}{2} = \frac{2x}{6} + \frac{2(2x-3y)}{6} + \frac{3(x+y)}{6}$

Step 2: Add the numerators and combine like terms. $= \frac{2x+4x-6y+3x+3y}{6} = \frac{9x-3y}{6}$

Step 3: Factor out the common term in the numerator and simplify the fraction. $= \frac{3(3x-y)}{6} = \frac{3x-y}{2}$ The simplified expression is $\boxed{\frac{3x-y}{2}}$.

3. Simplify $\frac{2a+4b}{4} - \frac{3(a-4b)}{6}$

Step 1: Simplify each fraction individually. $\frac{2a+4b}{4} = \frac{2(a+2b)}{4} = \frac{a+2b}{2}$ $\frac{3(a-4b)}{6} = \frac{a-4b}{2}$

Step 2: Substitute the simplified fractions and subtract the numerators. $= \frac{a+2b}{2} - \frac{a-4b}{2} = \frac{(a+2b)-(a-4b)}{2}$

Step 3: Distribute the negative sign and combine like terms. $= \frac{a+2b-a+4b}{2} = \frac{6b}{2}$

Step 4: Simplify the fraction. $= 3b$ The simplified expression is $\boxed{3b}$.

4. Simplify $\frac{3e+e^2}{4} + \frac{e}{3}$

Step 1: Find a common denominator for 4 and 3, which is 12. $\frac{3e+e^2}{4} + \frac{e}{3} = \frac{3(3e+e^2)}{12} + \frac{4e}{12}$

Step 2: Add the numerators and combine like terms. $= \frac{9e+3e^2+4e}{12} = \frac{3e^2+13e}{12}$ The simplified expression is $\boxed{\frac{3e^2+13e}{12}}$.

5. Simplify $\frac{5 \cdot 5+4}{8} - \frac{25-2}{4}$

Step 1: Calculate the numerators. $5 \cdot 5+4 = 25+4 = 29$ $25-2 = 23$

Step 2: Substitute the calculated numerators into the expression. $\frac{29}{8} - \frac{23}{4}$

Step 3: Find a common denominator for 8 and 4, which is 8. $= \frac{29}{8} - \frac{2 \cdot 23}{8} = \frac{29}{8} - \frac{46}{8}$

Step 4: Subtract the numerators. $= \frac{29-46}{8} = \frac{-17}{8}$ The simplified expression is $\boxed{-\frac{17}{8}}$. That's 2 down. 3 left today — send the next one.