How do you solve #\frac { x - 8} { 8- x } = - \frac { x + 9} { x - 9}#?

Question

732 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-21T01:44:19

No solutions for #x#

We first need to setup the conditions, that is #x!=8,9#, because that will make the fractions undefined.

#(x-8)/(8-x)=-(x+9)/(x-9)#

Multiplying both sides by #-1# gives us

#-(x-8)/(8-x)=(x+9)/(x-9)#

We can move the negative to the bottom side.

#(x-8)/-(8-x)=(x+9)/(x-9)#

#(x-8)/(x-8)=(x+9)/(x-9)#

#(x+9)/(x-9)=1#

#x+9=x-9#

#x+18=x#

From here, we find that there are no solutions for #x#, because if we subtract #x# from both sides, we will get #18=0#, which is impossible!