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4a) ( 10x+5 / 3x ) × ( 6x / 10 )= ( 10x + 5 ) ( 6x )
---------------------------
( 10 ) ( 3x )
= 5 ( 2x + 1) • 2 ( 3x )
------------------------------
5 ( 2) ( 3x )
= 2x + 1
b) ( 3x² + 2x ) • ( 14 )
------------------------------
( 7 ) • ( 5x )
= x ( 3x + 2) • 7 ( 2)
-----------------------------
7 • x ( 5 )
= 2 ( 3x + 2)
-------------------
5
= 6x + 4
--------------
5
c) ( 8 - 6x ) • ( 5y² )
---------------------------
( 3y ) • ( 2 )
= 2 ( 4 - 3x ) • y ( 5y )
--------------------------------
y ( 3 ) • 2
= ( 4 - 3x ) ( 5y )
------------------------
3
= 20y - 15xy
-------------------
3
5a) ( 10a-5 / 4b ) ÷ ( 5ab / 2)
= ( 10a - 5 ) • ( 2)
-------------------------
( 4b ) • ( 5ab )
= 5 ( 2a - 1) • ( 2)
--------------------------
5 ( ab ) • 2 ( 2b )
= 2a - 1
--------------
( ab ) ( 2b )
= 2a - 1
-------------
2ab
b) ( 32p²q² / 9r ) ÷ ( 4p²q / 3r² )
= ( 32p²q² ) • ( 3r² )
------------------------------
( 4p²q ) • ( 9r )
= ( 4p²q )( 8q ) • ( 3r )( r )
------------------------------------
( 4p²q ) • ( 3 )( 3r )
= ( 8q )( r )
----------------
3
= 8qr
---------
3
c ) ( 8xyz / 21 ) ÷ ( 4x²z / 9y )
= ( 8xyz ) • ( 9y )
------------------------
( 21 ) • ( 4x²z )
= ( 4xz )( 2y ) • ( 3 )( 3y )
-----------------------------------
( 4xz )( x ) • ( 3 )( 7 )
= ( 2y ) ( 3y )
------------------
( x ) ( 7 )
= 6y²
--------
7x