Answer:
a) and b) satisfied the condition of the given equation.
Step-by-step explanation:
Given: [tex]\frac{a}{(b + c)}[/tex] ≠ [tex]\frac{a}{b}[/tex] + [tex]\frac{a}{c}[/tex]
Then,
[tex]\frac{a}{(b + c)}[/tex] ≠ [tex]\frac{(ac + ab)}{bc}[/tex]
a) For a = 21, b = 4 and c = -2, then we have;
[tex]\frac{21}{(4 + (-2))}[/tex] ≠ [tex]\frac{(21*-2 + 21*4)}{4*-2}[/tex]
[tex]\frac{21}{4 - 2}[/tex] ≠ [tex]\frac{(-42 + 84)}{-8}[/tex]
[tex]\frac{21}{2}[/tex] ≠ [tex]\frac{42}{-8}[/tex]
[tex]\frac{21}{2}[/tex] ≠ [tex]-\frac{21}{4}[/tex]
Therefore the condition of the given equation is satisfied.
b) For a = 1, b = 10 and c = 1, then we have:
[tex]\frac{1}{(10 + 1)}[/tex] ≠ [tex]\frac{(1*1 + 1*10)}{10*1}[/tex]
[tex]\frac{1}{11}[/tex] ≠ [tex]\frac{(1 + 10)}{10}[/tex]
[tex]\frac{1}{11}[/tex] ≠ [tex]\frac{11}{10}[/tex]
Therefore the condition of the given equation is satisfied.
