374 alGEbra De mystif ieD
EXAMPLES
Solve the equation.
x
xx
−
−−
(^1) =−
28
2
(^25)
This is in the form “fraction = fraction” so we cross-multiply.
51 28
52416
2416
2
2
2
()2( )
5
xxx
xxx
xx
−=−−−
−=−++
+−− +−−
+−=
+−=
+= −=
2416
2210
273
30
2
2
xx
xx
xx
xx
()() 0
270
−− 77 ++
=− =
=−
33
27 3
7
2
xx
x
Solve the equation.
4
2
14
xx^22
x
− xx
- = −
−
We begin by factoring each denominator so that we can find the LCD. After
identifying the LCD, we will multiply each of the three terms by the LCD.
4
2
14
2
2
4
2
xx
x
xx
xx
xx
xx
xx
()
LCD()
(2)
1()
(
−
- = −
- = −
−
=−
− ⋅
−
- = −
- −− ⋅ + = − ⋅ −
−
+− +=−
+−−
2
1
124
2
4214
4 2
)()
1
()()
x
x
xx
x
xx x
xx 224
24
4
2
=−
−+=−
x
xx x
x
()()
++=
++=
+= +=
4
320
210
20 10
2
x
xx
xx
xx
−− −−
22 11
x −−= 21 x −
EXAMPLES
Solve the equation.
EXAMPLES
Solve the equation.