Question

Solve the equatuon

x/2-(2/(x+1))=1

x=?

Answer 1

`(x)/(2)-(2)/(x+1)=1`

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)

`(x)/(2)[2(x+1)]-(2)/(x+1)[2(x+1)] = 1[2(x+1)]`

Then shorten the fractions.

`(x)/(2)[2(x+1)]-(2)/(x+1)[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)`

Distribute in all.

`x^2+x-4=2x+2`

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.

`x^2+x-4-2x-2=0\\x^2-x-6=0\\`

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.)

`(x-3)(x+2)=0\\x=3,-2`

Thus, the answer is x = 3, -2