# How do you solve #(x+2)/(x+1)>0#?

##### 1 Answer

The "critical" values are

#### Explanation:

In order for the fraction as a whole to be greater than 0, both the numerator and the denominator will need to be greater than 0 (or less than 0), so that the division will yield a positive value.

We can think of the LHS as the product of two factors:

The first factor

The second factor

Next, we create a sign table for the factors and fill it in with

Factor - - - - - - - - - - - Sign - - - - - - -

. . . . . . . . .------- -2 ---------- -1 -----------

. . . . . . . . .-------------------------------------

To fill in the bottom row, simply multiply the signs of all the factor rows together.

Notice the

Finally, we pluck out the interval(s) over which the whole expression is greater than 0. After multiplying the signs in the sign table, we see that we get:

Our solution is: