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04 - 23- 23

ALGEBRA: Division of Algebraic Expressions
(Sample Problems & Solutions) - Part 008
1
...


of

the

following:

� �2 + 1 ÷

Solution:

Rewrite the expressions as follows,

�

�2

+1÷�

4

�2

+1

3

=

� �2 + 1

�4

�2 + 1

Simplifying further the expressions, we have,

� �2 + 1

�4

�
�3 ∙ �

�
�4

�2 + 1

3

�2 + 1
�2 + 1 3

�� + �
�2 + 1 2 ∙ � � + �

�
�
�3 �2 + 1
1
1
�3 �2 + 1
�
�� + ��

2

�
Therefore, the quotient of the given problem is � �
...
Simplify the following:

...

�

�2 �4 �3
3
...


Take the reciprocal of the second term, then proceed
to multiplication, so we have,
�2 �4 �3
���
÷
�+�
�+�

�+�
�2 �4 �3
×
�+�
���

Rewrite the expressions for further simplification as
follows,
�+�
� ∙ � ∙ �3 ∙ � ∙ �2 ∙ �
×
�+�
���

Then cancel out some expressions, such as,
�+�
� ∙ � ∙ �3 ∙ � ∙ �2 ∙ �
×
�+�
���
� ∙ �3 ∙ �2 �
×
�
�
��� ��

Therefore, the quotient of the given problem is ��� ��
...
Find the quotient:
Solution:

� �2 +�2
�+�

÷

�4 �2 +�2

�+� 2

−2

� � 2 + �2
�4 �2 + �2
÷
�+�
�+� 2

−2

� � 2 + �2
�� �� + ��
÷
�+�
�+� �

−�


...
Find the quotient of the following:
�2
Solution:

�4 �3
�5
÷ 4
�2
�

��

÷

�5

�4

�


...


Take the reciprocal of the second term, then proceed
to multiplication, so we have,

�4 �3
��
÷ �
�2
�
��
�4 �3
×
�2
��

Rewrite the expressions for further simplification as
follows,
�4 �3
×
�2
�4 �4
×
�2

�4

�5
�3
�5

� 4 ∙ �2 ∙ �2
�3
×
�5
�2

Then cancel out some expressions, such as,
�4 ∙ �2 ∙ ��
��
×
��
��
� 4 ∙ �2
�
×
�
��

�4 ∙ �2 �
×
�
�
3
2
� ∙�∙�
�
×
�
�
�� ��

Therefore, the quotient of the given problem is �� ��

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