Question

What is the product in simplest form state any restrictions on the variable x^2+7x+10/x+3?

Answer 1

`\cfrac{x^2+7x+10}{x+3 } = \cfrac{ (x + 5)(x + 2)}{x + 3} , x \\eq -3`

Answer 2

The expression given to us is:

`(x^2+7x+10)/(x+3)`

This can be rewritten as:

`(x^2+2x+5x+10)/(x+3)`

Now, let us take
`x` as the common factor in the first two terms in the numerator and 5 as the common factor in the last two terms in the numerator. Thus, we get:

`(x^2+2x+5x+10)/(x+3)=(x(x+2)+5(x+2))/(x+3)`

Now, taking
`(x+2)` as the common factor, we get:

`((x+2)(x+5))/((x+3))`

The above is the simplest form of the given expression,
`(x^2+7x+10)/(x+3)`

As we know that the denominator of a rational expression can never be zero, thus the only restriction in our case will be:

`x+3\\eq0`

or,
`x\\eq -3` (subtracting 3 from both sides)

Thus, the restriction is that
`x` cannot be equal to
`-3`.