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Kemal Halilović,profesor matematike Brčko
1
Algebarski racionalni izraziAlgebarski racionalni izraziAlgebarski racionalni izraziAlgebarski racionalni izrazi
Množenje Množenje Množenje Množenje
Množenje algebarskih razlomaka vrši se na isti način kao i množenje običnih razlomaka.
N.p.r.
21
10
7
5
3
2=⋅
5
12
5
43 =⋅
385
6
11
1
5
2
7
3=⋅⋅
Prilikom množenja razlomaka treba obratiti pažnju da li se može izvršiti skraćivanje
razlomaka:
20
3
4
3
5
1
16
15
25
4=⋅=⋅
6
7
2
7
3
1
4
7
3
2=⋅=⋅
3
10
3
52
12
58 =⋅=⋅
ZADACIZADACIZADACIZADACI
1. ( )( ) 3
2
yx
ba
ba3
yx2
yx
ba
b3a3
y2x2=
−−
⋅−−
=−−
⋅−−
2. ( ) ( )
( )( )
22x
1a3
1a3
2x2
2x
1a3
1a3
2x2
x2
a31
1a3
4x2=
−−
⋅−−
=−−−−
⋅−−
=−−
⋅−−
=
3. ( )( ) 1a
1
2
1a
1a1a
1
a10
1a
1a
a52 −
=+
⋅+−
=+
⋅−
( )( )( ) ba
a2
baba
baa2 22
+=
+−−
=
4. ( )( ) b
a
ba
ba
aab
baa
ba
ba
baa
aba22
22
22
22
22
22
23
23
=−+
⋅+−
=−+
⋅+−
5. ( )( ) 6a
3a
6a
3a
3a
6a
36a12a
9a6a
3a
6a2
2
2
2
+−
=+
−⋅
−+
=+++−
⋅−+
6. ( )( )( )
( )( )( )
( )( )( )1aa
1aa1a2
1aa
1aa1a
1a1a
1a2a2
aa
1a
1a
2a4a2 222
2
3
2
2
−+++
=−
++−⋅
+−++
=−−
⋅−++
7. ( ) ba
b6
ba
ab6
ab
ab
bab2a
ab6
b
1
a
12
2
22
2
+=
+⋅
+=
++⋅
+
8. ( ) ( )
( ) ( )=
+−−+
⋅++
=+
+−+⋅
+++−
=
−
++
⋅
++−
1x22
xx22x2
2x
1x2
1x22
1x2x1x2
2x
2x1x
2
x
1x2
1x1
2x
1x 2222
( ) ( )2x2
x2
1x22
x2
2x
1x2
+−
=+
−⋅
++
9. ( ) ( )
( )( )
( )( )
=−
⋅
−
−−+
+
−+=
−⋅
−−
+−
−+
+ xy
yx
yx
yxxx
yx
xyxx
xy
yx
yx
x
yx
x
yx
x
yx
x 22
2
2
2
222
2
2
2
2
( ) ( ) ( ) ( )=
−⋅
−+
+=
−⋅
−
+−+
+
−+xy
yx
yx
xy
yx
xy
xy
yx
yx
xyxx
yx
xxyx 22
22
22
2
22
2
22
( ) ( )( ) ( )
( )( )=
+−⋅
+−
−++=
xy
yxyx
yxyx
yxxyyxxy22
22 ( ) ( )[ ]( ) ( )
( )( )xy
yxyx
yxyx
yxyxxy22
22 +−⋅
+−
−++
( ) ( )( )( )
=−
+−+++=
+−−++
=22
222222
yx
yxy2xyxy2x
yxyx
yxyx=
−+
22
22
yx
y2x2
Kemal Halilović,profesor matematike Brčko
2
10. ( )( )( )( )
=−
+−+⋅
+−
−−
=
−
++⋅
−
−− 1a
21a1a
1a1a
a2
1a
1
1a
21a
1a
a2
1a
122242
( )( )( )( )
=−
+−+⋅
+−−+
1a
21a1a
1a1a
a21a22
2 ( )( )( )
( )( )( ) =
−+
⋅+−
−=
−+−
⋅+−
−1a
1a
1a1a
1a
1a
21a
1a1a
1a 2
22
22
22
2
1a
1
1
1
1a
1a2 +
=⋅−−
11. ( )
( )( )( ) ( )
( )( )
=−
+⋅
+++⋅
++−
=−
+⋅
+++⋅
+−
2
2
22
22
2
2
233
4
1x
1a2
1x1xx
a
1aa
1x1x
1x
2a2
1xxx
a
aa
1x
( )( )( ) ( )( )
( )( )
=−
+⋅
++⋅
++−
2
2
22
22
1x
1a2
1x1x
1
1a
1x1x ( )( )( ) 1x
2
1x
2
1x
1
1
1x1x2 −=
−⋅
+⋅
+−
12. ( ) ( ) ( )
( ) ( )=
+−
⋅−−−
+⋅
++−+
=+−
⋅+−−
+⋅
+−−+
2x
2x
2x2xx
1aa
1a
2x2xx
2x
2x
2xx2x
aa
1a
2xx2x2
2
23
223
( )( )( )( ) a
1
1
1
a
1
1
2x
2x
1x2x
a
1
1x2x2
2
=⋅⋅=+−
⋅−−
⋅−+
=
13. ( )( ) ( )( )
( ) a
b1
a
b1
1
1
1
1
a1a
b1b1
b1
a1a1
a1
aa1
aa
b1
b1
a1
a1
a1
2
22 −=
−⋅⋅=
++−
⋅++−
⋅−+−
=+−
⋅+−
⋅
−
+
14. ( )
=
++
+++
+++
⋅+−
6a5a
1
3a4a
2
2a3a
1
2
a123a222
2
=
+++
++++
++++
⋅++−
6a2a3a
1
3a3aa
2
2a2aa
1
2
a129a6a222
2
( ) ( ) ( ) ( ) ( ) ( )=
++++
++++
+++⋅
++3a23aa
1
1a31aa
2
1a21aa
1
2
9a6a 2
( )( )( ) ( )( ) ( )( )
=
+++
+++
++⋅
+2a3a
1
3a1a
2
2a1a
1
2
3a2 ( ) ( )
( )( )( )=
++++++++
⋅+
3a2a1a
1a2a23a
2
3a2
( )( ) ( )( )( )
( )( )( )
1a
3a2
2a1a
2a4
2
3a
2a1a
8a4
2
3a
2a1a
1a4a23a
2
3a
++
=++
+⋅
+=
+++
⋅+
=++
+++++⋅
+
15. ( )
=−+
⋅
+−−−
++
+=
−+
⋅
++
−+−
+++
+x23
3x2
3x2
2x31x4
3x2
x3x2
x23
3x2
3x2
2x3
3x2
1x4
9x12x4
x3x22
2
2
2
( )( )( )
( ) ( )( )=
−+−+−++
=−+
⋅+
+−++=
−+
⋅
+−
++
+=
x233x2
9x3x6x2x3x2
x23
3x2
3x2
3x23xx3x2
x23
3x2
3x2
3x
3x2
x3x2 22
2
2
2
2
( )( ) ( )( )( )( )( )( )
13x23x2
3x23x2
3x23x2
9x4
x233x2
9x4 22
−=−++−
−=−+−
−=
−+−
************************mogumogumogumoguććććeeee susususu š š š štamparsketamparsketamparsketamparske gregregregrešššškekekeke************************
