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 (3a+5b)/(4) + (9a+b)/(8) Step 1: Find a common denominator for 4 and 8, which is 8. (3a+5b)/(4) + (9a+b)/(8) = (2(3a+5b))/(8) + (9a+b)/(8) Step 2: Add the numerators and combine like terms. = (6a+10b+9a+b)/(8) = (15a+11b)/(8) The simplified expression is (15a+11b)/(8). 2. Simplify (2x)/(6) + (2x-3y)/(3) + (x+y)/(2) Step 1: Find a common denominator for 6, 3, and 2, which is 6. (2x)/(6) + (2x-3y)/(3) + (x+y)/(2) = (2x)/(6) + (2(2x-3y))/(6) + (3(x+y))/(6) Step 2: Add the numerators and combine like terms. = (2x+4x-6y+3x+3y)/(6) = (9x-3y)/(6) Step 3: Factor out the common term in the numerator and simplify the fraction. = (3(3x-y))/(6) = (3x-y)/(2) The simplified expression is (3x-y)/(2). 3. Simplify (2a+4b)/(4) - (3(a-4b))/(6) Step 1: Simplify each fraction individually. (2a+4b)/(4) = (2(a+2b))/(4) = (a+2b)/(2) (3(a-4b))/(6) = (a-4b)/(2) Step 2: Substitute the simplified fractions and subtract the numerators. = (a+2b)/(2) - (a-4b)/(2) = ((a+2b)-(a-4b))/(2) Step 3: Distribute the negative sign and combine like terms. = (a+2b-a+4b)/(2) = (6b)/(2) Step 4: Simplify the fraction. = 3b The simplified expression is 3b. 4. Simplify (3e+e^2)/(4) + (e)/(3) Step 1: Find a common denominator for 4 and 3, which is 12. (3e+e^2)/(4) + (e)/(3) = (3(3e+e^2))/(12) + (4e)/(12) Step 2: Add the numerators and combine like terms. = (9e+3e^2+4e)/(12) = (3e^2+13e)/(12) The simplified expression is (3e^2+13e)/(12). 5. Simplify (5 · 5+4)/(8) - (25-2)/(4) Step 1: Calculate the numerators. 5 · 5+4 = 25+4 = 29 25-2 = 23 Step 2: Substitute the calculated numerators into the expression. (29)/(8) - (23)/(4) Step 3: Find a common denominator for 8 and 4, which is 8. = (29)/(8) - (2 · 23)/(8) = (29)/(8) - (46)/(8) Step 4: Subtract the numerators. = (29-46)/(8) = (-17)/(8) The simplified expression is -(17)/(8). That's 2 down. 3 left today — send the next one.