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\(9!/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((1\times2\times3\times4\times5\times6\times7\times8\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((2\times3\times4\times5\times6\times7\times8\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((6\times4\times5\times6\times7\times8\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((24\times5\times6\times7\times8\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((120\times6\times7\times8\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((720\times7\times8\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((5040\times8\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\((40320\times9)/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\(362880/(9-3)!\times3!\times(9!/6!\times3!)\)

 

\(362880/6!\times3!\times(9!/6!\times3!)\)

 

\(362880/(1\times2\times3\times4\times5\times6)\times3!\times(9!/6!\times3!)\)

 

\(362880/(2\times3\times4\times5\times6)\times3!\times(9!/6!\times3!)\)

 

\(362880/(6\times4\times5\times6)\times3!\times(9!/6!\times3!)\)

 

\(362880/(24\times5\times6)\times3!\times(9!/6!\times3!)\)

 

\(362880/(120\times6)\times3!\times(9!/6!\times3!)\)

 

\(362880/720\times3!\times(9!/6!\times3!)\)

 

\(504\times3!\times(9!/6!\times3!)\)

 

\(504\times(1\times2\times3)\times(9!/6!\times3!)\)

 

\(504\times(2\times3)\times(9!/6!\times3!)\)

 

\(504\times6\times(9!/6!\times3!)\)

 

\(3024\times(9!/6!\times3!)\)

 

\(3024\times((1\times2\times3\times4\times5\times6\times7\times8\times9)/6!\times3!)\)

 

\(3024\times((2\times3\times4\times5\times6\times7\times8\times9)/6!\times3!)\)

 

\(3024\times((6\times4\times5\times6\times7\times8\times9)/6!\times3!)\)

 

\(3024\times((24\times5\times6\times7\times8\times9)/6!\times3!)\)

 

\(3024\times((120\times6\times7\times8\times9)/6!\times3!)\)

 

\(3024\times((720\times7\times8\times9)/6!\times3!)\)

 

\(3024\times((5040\times8\times9)/6!\times3!)\)

 

\(3024\times((40320\times9)/6!\times3!)\)

 

\(3024\times(362880/6!\times3!)\)

 

\(3024\times(362880/(1\times2\times3\times4\times5\times6)\times3!)\)

 

\(3024\times(362880/(2\times3\times4\times5\times6)\times3!)\)

 

\(3024\times(362880/(6\times4\times5\times6)\times3!)\)

 

\(3024\times(362880/(24\times5\times6)\times3!)\)

 

\(3024\times(362880/(120\times6)\times3!)\)

 

\(3024\times(362880/720\times3!)\)

 

\(3024\times(504\times3!)\)

 

\(3024\times(504\times(1\times2\times3))\)

 

\(3024\times(504\times(2\times3))\)

 

\(3024\times(504\times6)\)

 

\(3024\times3024\)

 

\(9144576\)

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Oct 28, 2016
 #1
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Oct 28, 2016
 #2
avatar+1904 
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Solve for a

 

\(\frac{a-1}{ab}=\frac{{1-a}^{-1}}{b}\)

 

\(\frac{a-1}{ab}=\frac{1-\frac{1}{{a}^{1}}}{b}\)

 

\(\frac{a-1}{ab}=\frac{1-\frac{1}{a}}{b}\)

 

\(\frac{a-1}{ab}\times b=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{b(a-1)}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{ab-1b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{ab-b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{ab}{ab}-\frac{b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(1-\frac{b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(1-\frac{1}{a}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(1-\frac{1}{a}=\frac{b(1-\frac{1}{a})}{b}\)

 

\(1-\frac{1}{a}=\frac{1b-\frac{1}{a}b}{b}\)

 

\(1-\frac{1}{a}=\frac{b-\frac{1}{a}b}{b}\)

 

\(1-\frac{1}{a}=\frac{b}{b}-\frac{\frac{1}{a}b}{b}\)

 

\(1-\frac{1}{a}=1-\frac{\frac{1}{a}b}{b}\)

 

\(1-\frac{1}{a}=1-\frac{1}{a}\)

 

\(1-\frac{1}{a}-1=1-\frac{1}{a}-1\)

 

\(\frac{1}{a}-0=1-\frac{1}{a}-1\)

 

\(\frac{1}{a}=1-\frac{1}{a}-1\)

 

\(\frac{1}{a}=\frac{1}{a}-0\)

 

\(\frac{1}{a}=\frac{1}{a}\)

 

\(\frac{1}{a}\times a=\frac{1}{a}\times a\)

 

\(\frac{a}{a}=\frac{1}{a}\times a\)

 

\(1=\frac{1}{a}\times a\)

 

\(1=\frac{1a}{a}\)

 

\(1=\frac{a}{a}\)

 

\(1=1\)

 

Becasue a disappears and you get a solution that is true, this means that a can be any number.  It can be written as (-∞, ∞) or it can be written as {a|a is all real numbers}.

 

Solve for b

 

\(\frac{a-1}{ab}=\frac{{1-a}^{-1}}{b}\)

 

\(\frac{a-1}{ab}=\frac{1-\frac{1}{{a}^{1}}}{b}\)

 

\(\frac{a-1}{ab}=\frac{1-\frac{1}{a}}{b}\)

 

\(\frac{a-1}{ab}\times b=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{b(a-1)}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{ab-1b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{ab-b}{ab}=\frac{1-\frac{1}{a}}{b}\times b\)

 

\(\frac{ab-b}{ab}=\frac{b(1-\frac{1}{a})}{b}\)

 

\(\frac{ab-b}{ab}=1(1-\frac{1}{a})\)

 

\(\frac{ab-b}{ab}=1-\frac{1}{a}\)

 

\(\frac{ab-b}{ab}\times ab=(1-\frac{1}{a})\times ab\)

 

\(\frac{ab(ab-b)}{ab}=(1-\frac{1}{a})\times ab\)

 

\(1(ab-b)=(1-\frac{1}{a})\times ab\)

 

\(ab-b=(1-\frac{1}{a})\times ab\)

 

\(ab-b=ab(1-\frac{1}{a})\)

 

\(ab-b=1ab-\frac{1}{a}ab\)

 

\(ab-b=ab-\frac{1}{a}ab\)

 

\(ab-b=ab-\frac{1ab}{a}\)

 

\(ab-b=ab-\frac{ab}{a}\)

 

\(ab-b=ab-1b\)

 

\(ab-b=ab-b\)

 

\(ab-b+b=ab-b+b\)

 

\(ab+0b=ab-b+b\)

 

\(ab+0=ab-b+b\)

 

\(ab=ab-b+b\)

 

\(ab=ab+0b\)

 

\(ab=ab+0\)

 

\(ab=ab\)

 

\(\frac{ab}{a}=\frac{ab}{a}\)

 

\(b=\frac{ab}{b}\)

 

\(b=b\)

 

Because b is equal to b, b can be any number.  It can be written as (-∞, ∞) or it can be written as {b|b is all real numbers}.

Oct 28, 2016

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