MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1984 AMC 12/AHSME
2
Simplification
Simplification
Source:
October 15, 2005
Problem Statement
If
x
,
y
x,y
x
,
y
and
y
−
1
x
y - \frac{1}{x}
y
−
x
1
are not 0, then
x
−
1
y
y
−
1
x
\frac{x - \frac{1}{y}}{y - \frac{1}{x}}
y
−
x
1
x
−
y
1
equals
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
x
y
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
y
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
x
y
−
y
x
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
x
y
−
1
x
y
<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span> \frac{x}{y}\qquad<span class='latex-bold'>(C) </span>\frac{y}{x}\qquad<span class='latex-bold'>(D) </span>\frac{x}{y} - \frac{y}{x}\qquad<span class='latex-bold'>(E) </span> xy - \frac{1}{xy}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
y
x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
x
y
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
y
x
−
x
y
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
x
y
−
x
y
1
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