Answer :
To solve the given expression [tex]\(\frac{u - 6v}{20v} + \frac{u + 6v}{20v}\)[/tex], let's proceed with a step-by-step approach:
1. Write down the original expression:
[tex]\[ \frac{u - 6v}{20v} + \frac{u + 6v}{20v} \][/tex]
2. Break the expression into two separate fractions:
[tex]\[ \frac{u - 6v}{20v} + \frac{u + 6v}{20v} \][/tex]
3. Combine the two fractions:
Since both fractions have the same denominator, we can combine the numerators over the common denominator:
[tex]\[ \frac{(u - 6v) + (u + 6v)}{20v} \][/tex]
4. Simplify the numerator:
Combine like terms in the numerator:
[tex]\[ (u - 6v) + (u + 6v) = u - 6v + u + 6v \][/tex]
[tex]\[ = u + u - 6v + 6v \][/tex]
[tex]\[ = 2u \][/tex]
5. Substitute the simplified numerator back into the fraction:
[tex]\[ \frac{2u}{20v} \][/tex]
6. Simplify the fraction:
Divide both the numerator and the denominator by their common factor, which is 2:
[tex]\[ \frac{2u}{20v} = \frac{u}{10v} \][/tex]
Therefore, the simplified result of the expression [tex]\(\frac{u - 6v}{20v} + \frac{u + 6v}{20v}\)[/tex] is:
[tex]\[ \boxed{\frac{u}{10v}} \][/tex]
Given the options provided, the correct choice is:
D) [tex]\(\frac{u}{10v}\)[/tex]
1. Write down the original expression:
[tex]\[ \frac{u - 6v}{20v} + \frac{u + 6v}{20v} \][/tex]
2. Break the expression into two separate fractions:
[tex]\[ \frac{u - 6v}{20v} + \frac{u + 6v}{20v} \][/tex]
3. Combine the two fractions:
Since both fractions have the same denominator, we can combine the numerators over the common denominator:
[tex]\[ \frac{(u - 6v) + (u + 6v)}{20v} \][/tex]
4. Simplify the numerator:
Combine like terms in the numerator:
[tex]\[ (u - 6v) + (u + 6v) = u - 6v + u + 6v \][/tex]
[tex]\[ = u + u - 6v + 6v \][/tex]
[tex]\[ = 2u \][/tex]
5. Substitute the simplified numerator back into the fraction:
[tex]\[ \frac{2u}{20v} \][/tex]
6. Simplify the fraction:
Divide both the numerator and the denominator by their common factor, which is 2:
[tex]\[ \frac{2u}{20v} = \frac{u}{10v} \][/tex]
Therefore, the simplified result of the expression [tex]\(\frac{u - 6v}{20v} + \frac{u + 6v}{20v}\)[/tex] is:
[tex]\[ \boxed{\frac{u}{10v}} \][/tex]
Given the options provided, the correct choice is:
D) [tex]\(\frac{u}{10v}\)[/tex]
