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

2 Answers
Aug 31, 2016

Answer:

#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#

Aug 31, 2016

Answer:

#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