Simplify the following: 1. (3a+4b)/(10) + (5a-b)/(4); 2. (6y−5x)/(10) − (2x+y)/(5) + x/(3); 3. (5t+1)/(9); 4…

Question

Simplify the following: 1. (3a+4b)/(10) + (5a-b)/(4); 2. (6y−5x)/(10) − (2x+y)/(5) + x/(3); 3. (5t+1)/(9); 4. (4u+5)/(4) − (3u−5)/(2); 5. (x−3)/(3) − (x+2)/(5)

ScanSolve AI Tutor · Accepted Answer

let's tackle the remaining problems.

Here are the solutions for problems 4 and 5:

4. Simplify $\frac{u+5}{4} - \frac{3u-5}{2}$

Find the least common multiple (LCM) of the denominators 4 and 2.
The LCM is 4.
Rewrite the second fraction with the common denominator.
$\frac{3u-5}{2} = \frac{2(3u-5)}{2 \times 2} = \frac{6u-10}{4}$
Subtract the fractions.
$\frac{u+5}{4} - \frac{6u-10}{4} = \frac{(u+5) - (6u-10)}{4}$
Distribute the negative sign and combine like terms in the numerator.
$\frac{u+5-6u+10}{4} = \frac{(u-6u) + (5+10)}{4}$ $\frac{-5u+15}{4}$
The simplified expression is $\boxed{\frac{-5u+15}{4}}$ .

5. Simplify $\frac{x-3}{3} - \frac{x+2}{5}$
Find the LCM of the denominators 3 and 5.
The LCM is 15.
Rewrite each fraction with the common denominator.
$\frac{x-3}{3} = \frac{5(x-3)}{5 \times 3} = \frac{5x-15}{15}$ $\frac{x+2}{5} = \frac{3(x+2)}{3 \times 5} = \frac{3x+6}{15}$
Subtract the fractions.
$\frac{5x-15}{15} - \frac{3x+6}{15} = \frac{(5x-15) - (3x+6)}{15}$
Distribute the negative sign and combine like terms in the numerator.
$\frac{5x-15-3x-6}{15} = \frac{(5x-3x) + (-15-6)}{15}$ $\frac{2x-21}{15}$
The simplified expression is $\boxed{\frac{2x-21}{15}}$ .

Simplify the following: 1. (3a+4b)/(10) + (5a-b)/(4); 2. (6y-5x)/(10) - (2x+y)/(5) + x/(3); 3. (5t+1)/(9); 4. (4u+5)/(4) - (3u-5)/(2); 5. (x-3)/(3) - (x+2)/(5)

Step-by-step solution

Find the least common multiple (LCM) of the denominators 4 and 2.

Rewrite the second fraction with the common denominator.

Subtract the fractions.

Distribute the negative sign and combine like terms in the numerator.

Find the LCM of the denominators 3 and 5.

Rewrite each fraction with the common denominator.

Subtract the fractions.

Distribute the negative sign and combine like terms in the numerator.

Still stuck on this one?

More Mathematics Questions