# How do you solve #(x+7)/(x-4)<0#?

##### 4 Answers

#### Explanation:

For

An

Proof:

However, if top and bottom are negative, it will be positive, and any

The solution is

#### Explanation:

Let

We can build the sign chart

Therefore,

graph{(x+7)/(x-4) [-41.1, 41.14, -20.54, 20.55]}

#### Explanation:

Given:

#(x+7)/(x-4) < 0#

Note that since the linear expressions

For large positive or negative values of

graph{(y-(x+7)/(x-4))(x-3.99+y*0.0001) = 0 [-19.55, 20.45, -10.12, 9.88]}

The answer is

#### Explanation:

First we have to calculate the domain of the rational expression. As the denominator cannot be zero, the excluded values are:

Now we can solve the inequality.

#(x+7)/(x-4)<0#

We can change the rational inequality to quadratic inequality by multiplying it by the square of the denominator:

#(x+7)(x-4)<0#

If we graph the quadratic function:

graph{(x-4)*(x+7) [-36.52, 36.52, -18.22, 18.35]}

we see that it takes negative values for