1. ## Divide/simplify expressions

Please help me check my answer for the following expressions: 1) Divide the following: (x^2 + 10x + 21) divided by (x + 7) I have x^2 + 3?
2) Simplify 9/y + 3 + 2y/y + 6 I have 2y^2+15y+54/(y+3)(y+6) ?

2. Originally Posted by jay1
Please help me check my answer for the following expressions: 1) Divide the following: (x^2 + 10x + 21) divided by (x + 7) I have x^2 + 3?
2) Simplify 9/y + 3 + 2y/y + 6 I have 2y^2+15y+54/(y+3)(y+6) ?
1. $\frac{x^2 + 10x + 21}{x + 7} = \frac{(x + 7)(x + 3)}{x + 7}$

$= x + 3$.

2. $\frac{9}{y} + 3 + \frac{2y}{y} + 6$

$= \frac{9}{y} + \frac{3y}{y} + \frac{2y}{y} + \frac{6y}{y}$

$= \frac{9 + 11y}{y}$

$= \frac{9}{y} + 11$.

3. Originally Posted by Prove It
1. $\frac{x^2 + 10x + 21}{x + 7} = \frac{(x + 7)(x + 3)}{x + 7}$

$= x + 3$.

2. $\frac{9}{y} + 3 + \frac{2y}{y} + 6$

$= \frac{9}{y} + \frac{3y}{y} + \frac{2y}{y} + \frac{6y}{y}$

$= \frac{9 + 11y}{y}$

$= \frac{9}{y} + 11$.
I apologize< I should've used parentheses on number 2; it should read: 9/(y+3) + 2y/(y+6)
Is my answer above correct in this case?

4. Yep, $\frac{2y^2+15y+54}{(y+3)(y+6)}$ is correct

By the way, you should use parentheses for both the numerator and the denominator.
i.e. (2y^2+15y+54)/((y+3)(y+6)).

2y^2+15y+54/(y+3)(y+6) could be interpreted as $2y^2+15y+\frac{54}{y+3}(y+6)$

Otherwise it's not hard to use Latex to write these problems; there's a thread on how to use it.