What is expand ((720!+719!)*720+359*721!)/(720*721!) ?

The solution to expand ((720!+719!)*720+359*721!)/(720*721!) is 1/721+1/519120+359/720

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expand ((720!+719!)720+359721!)/(720*721!)

expand

\frac{( 720 ! + 719 ! ) \cdot 720 + 359 \cdot 721 !}{720 \cdot 721 !}

\frac{1}{721} + \frac{1}{519120} + \frac{359}{720}

Decimal Notation

0.5

Solution steps

\frac{( 720 ! + 719 ! ) \cdot 720 + 359 \cdot 721 !}{720 \cdot 721 !}

Expand

(720! + 719!) \cdot 720 + 359 \cdot 721! : 720 \cdot 720! + 720 \cdot 719! + 359 \cdot 721!

= \frac{720 \cdot 720 ! + 720 \cdot 719 ! + 359 \cdot 721 !}{720 \cdot 721 !}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{720 \cdot 720 ! + 720 \cdot 719 ! + 359 \cdot 721 !}{720 \cdot 721 !} = \frac{720 \cdot 720 !}{720 \cdot 721 !} + \frac{720 \cdot 719 !}{720 \cdot 721 !} + \frac{359 \cdot 721 !}{720 \cdot 721 !}

= \frac{720 \cdot 720 !}{720 \cdot 721 !} + \frac{720 \cdot 719 !}{720 \cdot 721 !} + \frac{359 \cdot 721 !}{720 \cdot 721 !}

Cancel

\frac{720 \cdot 720 !}{720 \cdot 721 !} : \frac{1}{721}

= \frac{1}{721} + \frac{720 \cdot 719 !}{720 \cdot 721 !} + \frac{359 \cdot 721 !}{720 \cdot 721 !}

Cancel

\frac{720 \cdot 719 !}{720 \cdot 721 !} : \frac{1}{519120}

= \frac{1}{721} + \frac{1}{519120} + \frac{359 \cdot 721 !}{720 \cdot 721 !}

Cancel

\frac{359 \cdot 721 !}{720 \cdot 721 !} : \frac{359}{720}

= \frac{1}{721} + \frac{1}{519120} + \frac{359}{720}

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What is expand ((720!+719!)*720+359*721!)/(720*721!) ?
The solution to expand ((720!+719!)*720+359*721!)/(720*721!) is 1/721+1/519120+359/720