Question 179760
{{{((4x^2-1)/(16x+8))/((2x^2+x-1) /(5x^2-1))}}}
<pre><font size = 4 color = "indigo"><b>
Write the top fraction divided by the bottom
fraction:

{{{matrix(1,3,(4x^2-1) /(16x+8), "÷", (2x^2+x-1) /(5x^2-1))}}}

Invert the second fraction and change the 
division to multiplication:

{{{matrix(1,3,(4x^2-1) /(16x+8), "×", (5x^2-1)/(2x^2+x-1))}}}

Everything will factor except the {{{5x^2-1}}}, 
which should be written in parentheses:

{{{matrix(1,3,((2x-1)(2x+1)) /(8(2x+1)), "×", ((5x^2-1))/((2x-1)(x+1)))}}}

Indicate the multiplicaton of the numerators and 
the denominators all as one fraction:

{{{((2x-1)(2x+1)(5x^2-1))/(8(2x+1)(2x-1)(x+1))}}}

Cancel the {{{(2x-1)}}}'s

{{{(cross((2x-1))(2x+1)(5x^2-1))/(8(2x+1)cross((2x-1))(x+1))}}}

Cancel the {{{(2x+1)}}}'s

{{{(cross((2x-1))cross((2x+1))(5x^2-1))/(8cross((2x+1))cross((2x-1))(x+1))}}}

All that's left is:

{{{(5x^2-1)/(8(x+1))}}}

You can leave it that way or 
distribute out the bottom:

{{{(5x^2-1)/(8x+8)}}}

Edwin</pre>