Question

How do you solve `8/9=(n+6)/n`?

Answer 1

`n=-54`

Explanation:

When we have 1 fraction equal to another we can use the method of `color(blue)"cross-multiplication"` to solve.

This is performed as follows.

`color(blue)(8)/color(red)(9)=color(red)(n+6)/color(blue)(n)`

Now cross-multiply (X) the values on either end of an 'imaginary' cross and equate them.

That is multiply the `color(blue)"blue"` values together and the `color(red)"red"` values together and equate them.

`rArrcolor(red)(9(n+6))=color(blue)(8n)`

distribute the bracket

`rArr9n+54=8n`

subtract 8n from both sides

`rArr9n-8n+54=cancel(8n)-cancel(8n)rArrn+54=0`

subtract 54 from both sides

`rArrn+cancel(54)-cancel(54)=0-54`

`rArrn=-54`

Answer 2

`n=-54`

Explanation:

`(8/9) -((n+6)/n)=0`
Taking common denominator `9(n+1)` we have:

`(8n-9(n+6))/(9n)=0`
`9n!=0`so `n!=0`
`=(8n-9n-54)/(9n)`
`=(-n-54)/(9n)=0`
When the fraction equals zero so its numerator will be zero
So,
`-n-54=0`
`-n=54`
therefore, `n=-54` accepted