Answer:
Explanation:
First, we can write:
x
=
1
.
¯¯¯¯
21
Next, we can multiply each side by
100
giving:
100
x
=
121
.
¯¯¯¯
21
Then we can subtract each side of the first equation from each side of the second equation giving:
100
x
−
x
=
121
.
¯¯¯¯
21
−
1
.
¯¯¯¯
21
We can now solve for
x
as follows:
100
x
−
1
x
=
(
121
+
0
.
¯¯¯¯
21
)
−
(
1
+
0
.
¯¯¯¯
21
)
(
100
−
1
)
x
=
121
+
0
.
¯¯¯¯
21
−
1
−
0
.
¯¯¯¯
21
99
x
=
(
121
−
1
)
+
(
0
.
¯¯¯¯
21
−
0
.
¯¯¯¯
21
)
99
x
=
120
+
0
99
x
=
120
99
x
99
=
120
99
99
x
99
=
3
×
40
3
×
33
x
=
3
×
40
3
×
33
x
=
40
33