SOLUTION: Show each step in multiplying/dividing the following rational expressions: [(14x - 7)/(x^2 + 3x - 4)] · [(x^2 + 6x + 8)/(2x^2 + 5x - 3)] ÷ [(x^2 + 2x)/(x^2 + 2x - 3)]

  14x - 7      x2 + 6x + 8      x2 + 2x
----------- · ------------- ÷ -----------
x2 + 3x - 4   2x2 + 5x - 3    x2 + 2x - 3

Invert the divided fraction and change the division to
multiplication:

  14x - 7      x2 + 6x + 8    x2 + 2x - 3
----------- · ------------- · -----------
x2 + 3x - 4   2x2 + 5x - 3      x2 + 2x

Factor all numerators and denominators:

   7(2x - 1)    (x + 4)(x + 2)    (x + 3)(x - 1)
------------- · --------------- · --------------
(x + 4)(x - 1)  (x + 3)(2x - 1)      x(x + 2)

Write the product of the numerators over the product of 
the denominators:

7(2x - 1)(x + 4)(x + 2)(x + 3)(x - 1)
-------------------------------------
(x + 4)(x - 1)(x + 3)(2x - 1)x(x + 2)

Cancel the (2x - 1)'s

7(2x - 1)(x + 4)(x + 2)(x + 3)(x - 1)
-------------------------------------
(x + 4)(x - 1)(x + 3)(2x - 1)x(x + 2)

7(x + 4)(x + 2)(x + 3)(x - 1)
-----------------------------
(x + 4)(x - 1)(x + 3)x(x + 2)

Cancel the (x + 4)'s

7(x + 4)(x + 2)(x + 3)(x - 1)
-----------------------------
(x + 4)(x - 1)(x + 3)x(x + 2)

7(x + 2)(x + 3)(x - 1)
----------------------
(x - 1)(x + 3)x(x + 2)

Cancel the (x + 2)'s

7(x + 2)(x + 3)(x - 1)
----------------------
(x - 1)(x + 3)x(x + 2)

7(x + 3)(x - 1)
---------------
(x - 1)(x + 3)x

Cancel the (x - 1)'s

7(x + 3)(x - 1)
---------------
(x - 1)(x + 3)x
 
7(x + 3)
--------
(x + 3)x

Cancel the (x + 3)'s

7(x + 3)
--------
(x + 3)x

 7
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 x

Edwin
AnlytcPhil@aol.com