04/07/2025
04/07/2025
Bài 2. Thực hiện các phép tính sau:
x+2
x3
−1
⋅(x2
+x+1)
�3−1�+2⋅(�2+�+1)=(�−1)(�2+�+1)�+2⋅(�2+�+1)=(�−1)(�2+�+1)2�+2
x+2
x3
−1
⋅(x2
+x+1)=x+2
(x−1)(x2
+x+1)
⋅(x2
+x+1)=x+2
(x−1)(x2
+x+1)2
b) �4+2�2+1�2−2⋅�−12�+2⋅2�2−4(�2+1)2
x2
−2
x4
+2x2
+1
⋅2x+2
x−1
⋅(x2
+1)2
2x2
−4
�4+2�2+1�2−2⋅�−12�+2⋅2�2−4(�2+1)2=(�2+1)2�2−2⋅�−12(�+1)⋅2(�2−2)(�2+1)2=�−1�+1
x2
−2
x4
+2x2
+1
⋅2x+2
x−1
⋅(x2
+1)2
2x2
−4
=x2
−2
(x2
+1)2
⋅2(x+1)
x−1
⋅(x2
+1)2
2(x2
−2)
=x+1
x−1
c) �3+8�−1+10−2��+2+�3+8�−1+�−9�+2
x−1
x3
+8
+x+2
10−2x
+x−1
x3
+8
+x+2
x−9
�3+8�−1+10−2��+2+�3+8�−1+�−9�+2=2�3+8�−1+10−2�+�−9�+2=2�3+8�−1+1−��+2
x−1
x3
+8
+x+2
10−2x
+x−1
x3
+8
+x+2
x−9
=2x−1
x3
+8
+x+2
10−2x+x−9
=2x−1
x3
+8
+x+2
1−x
=2(�+2)(�2−2�+4)�−1+1−��+2=2(�+2)(�2−2�+4)�−1−�−1�+2
=2x−1
(x+2)(x2
−2x+4)
+x+2
1−x
=x−1
2(x+2)(x2
−2x+4)
−x+2
x−1
d) �2−3�+2�2−5�+6⋅�2−�−6�2−2�+1
x2
−5x+6
x2
−3x+2
⋅x2
−2x+1
x2
−x−6
�2−3�+2�2−5�+6⋅�2−�−6�2−2�+1=(�−1)(�−2)(�−2)(�−3)⋅(�−3)(�+2)(�−1)2=�+2�−1
x2
−5x+6
x2
−3x+2
⋅x2
−2x+1
x2
−x−6
=(x−2)(x−3)
(x−1)(x−2)
⋅(x−1)2
(x−3)(x+2)
=x−1
x+2
Bài 3. Thu gọn biểu thức:
A=(x2
−4
x
+x+2
1
−x−2
2
)⋅(1−x+2
x
�=(�(�−2)(�+2)+1�+2−2�−2)⋅(�+2−��+2)
A=((x−2)(x+2)
x
+x+2
1
−x−2
2
)⋅(x+2
x+2−x
=(�+(�−2)−2(�+2)(�−2)(�+2))⋅2�+2=�+�−2−2�−4(�−2)(�+2)⋅2�+2
=((x−2)(x+2)
x+(x−2)−2(x+2)
)⋅x+2
2
=(x−2)(x+2)
x+x−2−2x−4
⋅x+2
2
=−6(�−2)(�+2)⋅2�+2=−12(�−2)(�+2)2
=(x−2)(x+2)
−6
⋅x+2
2
=(x−2)(x+2)2
−12
�=(2��−3+��+3+2�2+3�+19−�2)⋅�−1�+3
B=(x−3
2x
+x+3
x
+9−x2
2x2
+3x+1
)⋅x+3
x−1
�=(2��−3+��+3−2�2+3�+1�2−9)⋅�−1�+3
B=(x−3
2x
+x+3
x
−x2
−9
2x2
+3x+1
)⋅x+3
x−1
=(2�(�+3)+�(�−3)−(2�2+3�+1)(�−3)(�+3))⋅�−1�+3
=((x−3)(x+3)
2x(x+3)+x(x−3)−(2x2
+3x+1)
)⋅x+3
x−1
=2�2+6�+�2−3�−2�2−3�−1(�−3)(�+3)⋅�−1�+3=�2−1(�−3)(�+3)⋅�−1�+3
=(x−3)(x+3)
2x2
+6x+x2
−3x−2x2
−3x−1
⋅x+3
x−1
=(x−3)(x+3)
x2
−1
⋅x+3
x−1
=(�−1)(�+1)(�−3)(�+3)⋅�−1�+3=(�−1)2(�+1)(�−3)(�+3)2
=(x−3)(x+3)
(x−1)(x+1)
⋅x+3
x−1
=(x−3)(x+3)2
(x−1)2
(x+1)
�=1�+2+5�−2+4�2−4−6�+3
C=x+2
1
+x−2
5
+x2
−4
4
−x+3
6
�=1�+2+5�−2+4(�−2)(�+2)−6�+3
C=x+2
1
+x−2
5
+(x−2)(x+2)
4
−x+3
6
=(�−2)+5(�+2)+4(�−2)(�+2)−6�+3=�−2+5�+10+4(�−2)(�+2)−6�+3
=(x−2)(x+2)
(x−2)+5(x+2)+4
−x+3
6
=(x−2)(x+2)
x−2+5x+10+4
−x+3
6
=6�+12(�−2)(�+2)−6�+3=6(�+2)(�−2)(�+2)−6�+3=6�−2−6�+3
=(x−2)(x+2)
6x+12
−x+3
6
=(x−2)(x+2)
6(x+2)
−x+3
6
=x−2
6
−x+3
6
=6(�+3)−6(�−2)(�−2)(�+3)=6�+18−6�+12(�−2)(�+3)=30(�−2)(�+3)
=(x−2)(x+3)
6(x+3)−6(x−2)
=(x−2)(x+3)
6x+18−6x+12
=(x−2)(x+3)
30
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