Question

I was wondering if someone could help me figure this question out?

Answer 1

Hey there @veeveeniko ,
First you'll need to find the common denominator which is x²+x in our case :
\[\frac{ x-6 }{ x+1 }*\frac{ x }{ x }=\frac{ x²-6x }{ x²+x }\]
You'll get:\[\frac{ x²-5x+4 }{ x²+x }=0\]
x²+x must be different than 0 so : \[x \in \mathbb{R}-\left\{ 0,-1 \right\}\] Then you solve x²-5x+4=0 like you'd solve any normal quadratic equation and check that your solutions belong in \[\mathbb{R}-\left\{ 0,-1 \right\}\]\

Answer 2

I'm terribly sorry @math&ing001 but I'm still really confused.

Answer 3

Which part are you confused about ?

Answer 4

So for the first part you found the common denominator but how'd you get the first part from the original equation?

Answer 5

When you put it in common denominator it first looks like this : \[\frac{ x+5 }{ x²+x }=\frac{ 1-(x²-6x) }{ x²+x }\] Then you take all terms to one side, so as to make it a regular quadratic equation.

Answer 6

Alright, that makes sense I think.