Sure! Let's solve each part of the problem step-by-step:
### First Equation: [tex]\( 3 \frac{8}{a} - \frac{3}{a} = 0 \)[/tex]
1. Let's start with the equation [tex]\( 3 \frac{8}{a} - \frac{3}{a} \)[/tex].
2. Notice that both terms have the common denominator [tex]\( a \)[/tex].
3. Simplify the expression inside the equation:
[tex]\[
3 \frac{8}{a} = \frac{24}{a}
\][/tex]
[tex]\[
\frac{3}{a} \text{ remains the same}
\][/tex]
4. Combine the terms:
[tex]\[
\frac{24}{a} - \frac{3}{a} = \frac{24 - 3}{a} = \frac{21}{a}
\][/tex]
5. Set the expression equal to 0:
[tex]\[
\frac{21}{a} = 0
\][/tex]
6. [tex]\( \frac{21}{a} \)[/tex] equals zero if and only if [tex]\( 21 = 0 \)[/tex], which is impossible.
7. Therefore, there are no solutions for [tex]\( a \)[/tex] in this equation.
### Second Equation: [tex]\( 4 \frac{5}{11} - \frac{3}{4} \)[/tex]
1. First, compute [tex]\( 4 \frac{5}{11} \)[/tex]:
[tex]\[
4 \cdot \frac{5}{11} = \frac{20}{11}
\][/tex]
2. Next, consider the term [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
\frac{3}{4} \text{ remains the same}
\][/tex]
3. Subtract [tex]\( \frac{3}{4} \)[/tex] from [tex]\( \frac{20}{11} \)[/tex]:
[tex]\[
\frac{20}{11} - \frac{3}{4}
\][/tex]
4. In order to subtract these fractions, find a common denominator. The least common multiple of 11 and 4 is 44. Convert each fraction:
[tex]\[
\frac{20}{11} = \frac{20 \times 4}{11 \times 4} = \frac{80}{44}
\][/tex]
[tex]\[
\frac{3}{4} = \frac{3 \times 11}{4 \times 11} = \frac{33}{44}
\][/tex]
5. Subtract the converted fractions:
[tex]\[
\frac{80}{44} - \frac{33}{44} = \frac{80 - 33}{44} = \frac{47}{44}
\][/tex]
Therefore, the solution to the second equation is [tex]\( \frac{47}{44} \)[/tex].
