Factorial!

Number Theory Level 1

10 ! − 9 ! 10 ! + 9 ! = ? \cfrac { \color{#20A900}{10!}-\color{#69047E}{9!} }{ \color{#20A900}{10!}+\color{#69047E}{9!} } = \ \color{#D61F06}?

10 11 \frac { 10}{11} 9 11 \frac { 9}{11} 10 9 \frac {10}{9} 9 10 \frac {9}{10}

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Sarthak Sharma by Sarthak Sharma , 21, Canada

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5 solutions

Sarthak Sharma
Aug 4, 2014

10 ! − 9 ! 10 ! + 9 ! = 9 ! ( 10 − 1 ) 9 ! ( 10 + 1 ) = 10 − 1 10 + 1 = 9 11 \cfrac { 10!-9! }{ 10!+9! } =\cfrac { 9!(10-1) }{ 9!(10+1) } =\cfrac { 10-1 }{ 10+1 } =\cfrac { 9 }{ 11 }

29 Helpful 0 Interesting 0 Brilliant 0 Confused

That is it.

Dladla Arthur - 6 years, 9 months ago

Oh my goodness!!! This is really a simple solution!!!

Sahba Hasan - 6 years, 8 months ago

Yeah! Was simple!

Anik Mandal - 6 years, 10 months ago
Adam Zaim
Sep 16, 2014

Let 9!=a

Since 10!=10*9!

10!=10a

(10a-a)/(10a+a)=(9a)/(11a)=9/11

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Saurabh Desale
Aug 24, 2014

(10-1)×9!/(10+1)×9!=9/11

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishal S
Aug 13, 2015

Let 9!=x

The expression becomes (10x-x)/(10x+x) =9x/11x =9/11

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Write a solution. 9!(10-1)/9!(10+1)=9/11

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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