Question

What is the simplified form of 1 over x minus 2 over x squared plus x ?

Answer 1

Answer: The simplified form is
`(x-1)/(x(x+1))`.

Explanation:

Given expression
`(1)/(x) -(2)/(x^2+x)`.

Let is factor second denominator
`x^2+x` first.

Factoring out GCF x we get

`x^2+x= x(x+1)`

Rewriting the equation

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

Now, we need to find the lowest common denominator of x and x(x+1).

The lowest common denominator of x and x(x+1) is x(x+1).

So, we need to multiply first fraction by (x+1) in top and bottom to get lowest common denominator x(x+1) under first fraction.

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

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

We got denominators same.

Therefore, subtracting numerators, we get

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

`(x-1)/(x(x+1))`.

Therefore, simplified form is
`(x-1)/(x(x+1))`.