Simplifying fractionsHow to transform(1+1−4ab2a)n−(1−1−4ab2a)n(1+1−4ab2a)m−(1−1−4ab2a)minto(ba)n−1(ba)m−1Thanks.Added: As per comments, there is an additional assumption that a,b&gt;0,b=1−a, and b&gt;a.

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Simplifying fractionsHow to transform(1+1−4ab2a)n−(1−1−4ab2a)n(1+1−4ab2a)m−(1−1−4ab2a)minto(ba)n−1(ba)m−1Thanks.Added: As per comments, there is an additional assumption that a,b&amp;gt;0,b=1−a, and b&amp;gt;a.

jeffster830gyz · Accepted Answer

With the added information, which is keyIf&amp;nbsp;b=1−a&amp;nbsp;and&amp;nbsp;b&amp;gt;a,&amp;nbsp;then&amp;nbsp;1−a&amp;gt;a&amp;nbsp;so&amp;nbsp;1&amp;gt;2a.&amp;nbsp;Then1−4ab=1−4a(1−a)=1−4a+4a2=(1−2a)2,and since&amp;nbsp;1−2a&amp;gt;0, we have1−4ab=(1−2a)2=|1−2a|=1−2a.So1+1−4ab2a=1+(1−2a)2a=2(1−a)2a=ba1−1−4ab2a=1−(1−2a)2a=2a2a=1.That means that(1+1-4ab/2a)n-(1-1-4ab/2a)n/(1+1-4ab/2a)m-(1-1-4ab/2a)m=(ba)n-1n(ba)m-1m=(ba)n−1(ba)m−1.

mandamosppy · Accepted Answer

If a=0.1,b=0.2,n=5,m=2 I find the top fraction to be 940.4 and the second 10.333 so such a transformation won&#039;t work.

Simplifying fractions How to transform {(1+\sqrt{1-4ab}/2a)^n-(1-\sqrt{1-4ab}/2a)^n}/ {(1+\sqrt{1-4ab}/2a)^m-(1-\sqrt{1-4ab}/2a)^m} into {(b/ a)^n -1}/{(b/a)^m -1} Thanks. Added: As per

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