Answers and Explanations 129
Answers
1–100
6.
6
4
1
2
x
x
−
−
You need a common denominator so you can subtract the fractions. The least
common multiple of the denominators is (x – 1)(x + 1) = x
2
– 1, so multiply each
fraction accordingly to get this denominator. Then perform the arithmetic in
the numerator:
x
x
x
x
x x
x
x
x
x
x
x
x
x
x
−
− −
+
=
+
−
+
−
−
−
+
−
=
+
−
1
4
1
1
1
1
4
1
1
1
1
2
2
(
)
(
)(
)
(
)(
)
(
)(
)
− −
−
+
−
=
+ −
−
+
(
)
−
=
+ − +
−
−
=
−
−
x
x
x
x
x x
x
x
x
x x
x
x
x
x
2
2
2
2
2
2
2
2
2
5
4
1
5
4
1
5
4
1
6
4
1
7.
(
)
x
y
x
−1
Begin by factoring the expressions completely. Cancel any common factors and then
simplify to get the answer:
x
xy
y
x
x
x
xy
y
x
x
2
2
3
2
3
1
1
1
1
1
−






+






=
+
−






+






=
(
)(
)
( − − 





=
−
1
1
1
)
(
)
x
y
x
y
x