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)/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))/(2 · 4) + (9a+b)/(8) Step 2: Rewrite the first fraction with the common denominator. = (6a+10b)/(8) + (9a+b)/(8) Step 3: Add the numerators and combine like terms. = (6a+10b+9a+b)/(8) = ((6a+9a)+(10b+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))/(2 · 3) + (3(x+y))/(3 · 2) Step 2: Rewrite each fraction with the common denominator. = (2x)/(6) + (4x-6y)/(6) + (3x+3y)/(6) Step 3: Add the numerators and combine like terms. = (2x+4x-6y+3x+3y)/(6) = ((2x+4x+3x)+(-6y+3y))/(6) = (9x-3y)/(6) Step 4: 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 back into the expression. (a+2b)/(2) - (a-4b)/(2) Step 3: Subtract the numerators since they have a common denominator. = ((a+2b)-(a-4b))/(2) = (a+2b-a+4b)/(2) Step 4: Combine like terms. = ((a-a)+(2b+4b))/(2) = (6b)/(2) Step 5: Simplify the fraction. = 3b The simplified expression is 3b. 4. Simplify (3e+e^2)/(4) + (e)/(3) (Assuming the operation between the two fractions is addition, as it is a common convention when an operator is missing in such problems.) Step 1: Find a common denominator for 4 and 3, which is 12. (3e+e^2)/(4) + (e)/(3) = (3(3e+e^2))/(3 · 4) + (4e)/(4 · 3) Step 2: Rewrite each fraction with the common denominator. = (9e+3e^2)/(12) + (4e)/(12) Step 3: Add the numerators and combine like terms. = (9e+3e^2+4e)/(12) = (3e^2+(9e+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 back into the expression. (29)/(8) - (23)/(4) Step 3: Find a common denominator for 8 and 4, which is 8. = (29)/(8) - (2 · 23)/(2 · 4) Step 4: Rewrite the second fraction with the common denominator. = (29)/(8) - (46)/(8) Step 5: Subtract the numerators. = (29-46)/(8) = (-17)/(8) The simplified expression is -(17)/(8). Send me the next one 📸