Question

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

Answer 1

The expression given to us is:

$\frac{x^2+7x+10}{x+3}$

This can be rewritten as:

$\frac{x^2+2x+5x+10}{x+3}$

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:

$\frac{x^2+2x+5x+10}{x+3}=\frac{x(x+2)+5(x+2)}{x+3}$

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

$\frac{(x+2)(x+5)}{(x+3)}$

The above is the simplest form of the given expression, $\frac{x^2+7x+10}{x+3}$

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

$x+3\neq0$

or, $x\neq -3$ (subtracting 3 from both sides)

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

Answer 2

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