`(5^-1 + x^-1)/((5+x)*5^-1)`  

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violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

We can `1/5+1/x/(5+x)*1/x`

Multiplying the top and bottom by the lcd which is 5x:

`((5x*1/5)+(5x*1/x))/(5x((5+x)/x))`

Cancelling common factors. 

`(x+5)/(5(5+x))`

Addition is Cummutative, so we can rewrite the bottom as 5(x + 5).

`(x+5)/(5(x+5))`

We can cancel the (x + 5) on top and bottom. 

So, we will be left with 1/5, which is the answer.

 

I am sorry, I missed the bottom part, its 5^-1.

So, bottom will becomes x(5+x).

And cancelling the (x + 5), the answer will be 1/x.

My apologies.

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

`(5^(-1)+x^(-1))=(1/5)+(1/x)=(x+5)/(5x)`

`(5+x)5^(-1)=(5+x)/5`

`((x+5)/(5x))/((5+x)/5)=(5(5+x))/(5x(5+x))=1/x`

 

 

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