Question 865423
{{{((x^2-5x-4)/(x^2-1))/((4x^2-4)/(4x^2-8x+4))}}} Start with the given expression.



{{{((x^2-5x-4)/(x^2-1))*((4x^2-8x+4)/(4x^2-4))}}} Multiply the first fraction by the reciprocal of the second.



{{{((x^2-5x-4)/((x-1)(x+1)))*((4x^2-8x+4)/(4x^2-4))}}} Factor {{{x^2-1}}}



{{{((x^2-5x-4)/((x-1)(x+1)))*((4*(x-1)(x-1))/(4x^2-4))}}} Factor {{{4x^2-8x+4}}}



{{{((x^2-5x-4)/((x-1)(x+1)))*((4*(x-1)(x-1))/(4(x-1)(x+1)))}}} Factor {{{4x^2-4}}}



{{{((x^2-5x-4)/((x-1)(x+1)))*((4*highlight((x-1))(x-1))/(4*highlight((x-1))(x+1)))}}} Highlight a set of common terms (one term in the numerator, an equal term in the denominator)



{{{((x^2-5x-4)/((x-1)(x+1)))*((4*cross((x-1))(x-1))/(4*cross((x-1))(x+1)))}}} Cancel that pair of common terms



{{{((x^2-5x-4)/((x-1)(x+1)))*((4(x-1))/(4(x+1)))}}} Remove those cancellations.



{{{((x^2-5x-4)/(highlight((x-1))(x+1)))*((4*highlight((x-1)))/(4(x+1)))}}} Highlight another set of common terms



{{{((x^2-5x-4)/(cross((x-1))(x+1)))*((4*cross((x-1)))/(4(x+1)))}}} Cancel that pair of common terms



{{{((x^2-5x-4)/(x+1))*(4/(4(x+1)))}}} Remove those cancellations.
 


{{{((x^2-5x-4)/(x+1))*(highlight(4)/(highlight(4)(x+1)))}}} Highlight another set of common terms



{{{((x^2-5x-4)/(x+1))*(cross(4)/(cross(4)(x+1)))}}} Cancel that pair of common terms



{{{((x^2-5x-4)/(x+1))*(1/(x+1))}}} Remove those cancellations.



{{{((x^2-5x-4)*1)/((x+1)(x+1))}}} Multiply the fractions



{{{(x^2-5x-4)/(x^2+2x+1)}}} Expand and simplify


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Final Answer



{{{((x^2-5x-4)/(x^2-1))/((4x^2-4)/(4x^2-8x+4))}}}



simplifies to 



{{{(x^2-5x-4)/(x^2+2x+1)}}}



Optionally, you can have the denominator factored to have either {{{(x^2-5x-4)/((x+1)(x+1))}}} or {{{(x^2-5x-4)/((x+1)^2)}}}