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…

Question

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

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

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

Find a common denominator for 4 and 8, which is 8.
$\frac{3a+5b}{4} + \frac{9a+b}{8} = \frac{2(3a+5b)}{8} + \frac{9a+b}{8}$
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 $\frac{2x}{6} + \frac{2x-3y}{3} + \frac{x+y}{2}$
Find a common denominator for 6, 3, and 2, which is 6.
$\frac{2x}{6} + \frac{2x-3y}{3} + \frac{x+y}{2} = \frac{2x}{6} + \frac{2(2x-3y)}{6} + \frac{3(x+y)}{6}$
Add the numerators and combine like terms.
$= \frac{2x+4x-6y+3x+3y}{6} = \frac{9x-3y}{6}$
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 $\frac{2a+4b}{4} - \frac{3(a-4b)}{6}$
Simplify each fraction individually.
$\frac{2a+4b}{4} = \frac{2(a+2b)}{4} = \frac{a+2b}{2}$ $\frac{3(a-4b)}{6} = \frac{a-4b}{2}$
Substitute the simplified fractions and subtract the numerators.
$= \frac{a+2b}{2} - \frac{a-4b}{2} = \frac{(a+2b)-(a-4b)}{2}$
Distribute the negative sign and combine like terms.
$= \frac{a+2b-a+4b}{2} = \frac{6b}{2}$
Simplify the fraction.
$= 3b$
The simplified expression is $\boxed{3b}$ .

4. Simplify $\frac{3e+e^2}{4} + \frac{e}{3}$
Find a common denominator for 4 and 3, which is 12.
$\frac{3e+e^2}{4} + \frac{e}{3} = \frac{3(3e+e^2)}{12} + \frac{4e}{12}$
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 $\frac{5 \cdot 5+4}{8} - \frac{25-2}{4}$
Calculate the numerators.
$5 \cdot 5+4 = 25+4 = 29$ $25-2 = 23$
Substitute the calculated numerators into the expression.
$\frac{29}{8} - \frac{23}{4}$
Find a common denominator for 8 and 4, which is 8.
$= \frac{29}{8} - \frac{2 \cdot 23}{8} = \frac{29}{8} - \frac{46}{8}$
Subtract the numerators.
$= \frac{29-46}{8} = \frac{-17}{8}$
The simplified expression is $\boxed{-\frac{17}{8}}$ .

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

Step-by-step solution

Find a common denominator for 4 and 8, which is 8.

Add the numerators and combine like terms.

Find a common denominator for 6, 3, and 2, which is 6.

Add the numerators and combine like terms.

Factor out the common term in the numerator and simplify the fraction.

Simplify each fraction individually.

Substitute the simplified fractions and subtract the numerators.

Distribute the negative sign and combine like terms.

Simplify the fraction.

Find a common denominator for 4 and 3, which is 12.

Add the numerators and combine like terms.

Calculate the numerators.

Substitute the calculated numerators into the expression.

Find a common denominator for 8 and 4, which is 8.

Subtract the numerators.

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