Answer:
Option D. is the answer.
Step-by-step explanation:
The given statement is [tex]\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}[/tex]
Now we have to find a counter example from the given options that the statement is False.
A. a = 3, b = 5, c = -3, d = 5
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}[/tex]=[tex]\frac{3}{5}+\frac{-3}{5}=\frac{3-3}{5+5}[/tex]
0 = 0
So the given statement is true.
B. a = 0, b = 4, c = 0, d= 9
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}[/tex]
0 + 0 = 0
So for this example the given statement is true.
C. a = -2, b = 1, c = 2, d = 1
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}[/tex]
[tex]\frac{-2}{1}+\frac{2}{1}=\frac{-2+2}{1+1}[/tex]
0 = 0
Statement is true for these values.
D. a = 1, b = 2, c = 1, d = 2
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}[/tex]
[tex]\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2+2}[/tex]
[tex]1=\frac{1}{2}[/tex]
Therefore, for these values of a, b, c and d, the given statement is False.
Option D. is the answer.
