218 algebra De mystif ieD
6.^13
1 2 1
2
xx− 1 x−
+=
−13
1 112
xx− 1 xx−
+=
()−+()The LCD is (x − 1)(x + 1).()() ()()
()(xx
xxxx
xx−+
−−
+
(^11) =− +⋅−+
1
1
2
1
11 3
11 ))
()()
()
xx ()()
x
xx
x
xx
−+⋅
−
−− +⋅
=
+− −
111
1
112
1
3
1( 1) 2( 1))3
12 23
33
33
0
0
+− +=
−+=
−−
−=
xx
x
x
x
(0 and −0 are the same number)
- (2x − 1)^2 − 4x^2 = −4x + 1
(2x − 1)(2x − 1) −4x^2 = −4x + 1
4 x^2 − 2x − 2x + 1 − 4x^2 = −4x +1
−4x + 1 = −4x + 1
The last equation is true for any real number x. An equation true for any
real number x is called an identity. For example, (2x − 1)^2 − 4x^2 = − 4x + 1
is an identity. - 71 x+= 13
7113
71169
11
7 168
168
7
24
(^22)
x
x
x
x
x
+ =
+=
−−
=
- x^
xbefore
−=
−=610
61 0Isolate thesquareroot squarringbothsides.
++
=
[]=
=66
16
16
256(^22)
x
x
x