[tex]\frac{x}{2}-\frac{2}{x+1}=1[/tex]
We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.
Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)
[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)][/tex]
Then shorten the fractions.
[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)[/tex]
Distribute in all.
[tex]x^2+x-4=2x+2[/tex]
We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.
[tex]x^2+x-4-2x-2=0\\x^2-x-6=0\\[/tex]
We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)
[tex](x-3)(x+2)=0\\x=3,-2[/tex]
Thus, the answer is x = 3, -2
