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homework question that asks to perform the multiplication and division and simplification.

$$\frac{x^2+7x+10}{x^2+5x+4} \times \frac{x^2+3x+2}{x^2+4x+4} =$$

$$\frac{(x+5)(x+2)}{(x+4)(x+1)} \times \frac{(x+1)(x+2)}{(x+2)(x+2)} =$$

$$ = \frac{(x+5)}{(x+4)}$$

is my working out and answer correct?

I am typing this extra sentence in order to meet your quality standards!!!

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Correct answer. ! Don't worry. everything at the right place. – Manoj Pandey Mar 27 '13 at 8:41
Just to impress your teacher, you can also add condition after your answer saying : x not equal to ${-1,-2,-4}$ – lsp Mar 27 '13 at 8:45
what do you mean? – Ben Mar 27 '13 at 8:49
When you cancel something out, it is better to mention the condition that the term you are cancelling is not equal to zero. – lsp Mar 27 '13 at 8:50
lol, if I do that, she will become instantly suspicious. – Ben Mar 27 '13 at 9:11

Yes, it is correct. The $x+2$'s and $x+1$ terms do cancel. If there was no multiplication, the second part would be $\frac{x+1}{x+2}$, and the left side would be as is. However, you're OK.

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Yes, it is correct because you are able to cancel out two of the binomials leaving $(x+5)$ on the top and $(x+4)$ on the bottom.

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