Joseph wants to mulch his garden. His garden is x^{2} + 18x + 81 ft^{2}. One bag of mulch covers x^{2} - 81 ft^{2}. Divide the expressions and simplify to find how many bags of mulch Joseph needs to mulch his garden.

GAMEMASTERX40 Oct 2, 2018

#1**+4 **

If you read CPhill's solution to the previous problem, it will make it easier to understand.

Again, factor the numerator and the denominator! This a key factor for solving these types of problems!

For the numerator, we have \(x^2+18x+81\), and that changes into \(\left(x+9\right)^2\) after factoring.

Now, for the denominator, we have \(\:x^2-81\), and that changes into \(\left(x+9\right)\left(x-9\right)\) after factoring.

So, we have \(\frac{\left(x+9\right)^2}{\left(x+9\right)\left(x-9\right)}\) and that yields our final answer as \(\boxed{\frac{x+9}{x-9}}\).

tertre Oct 2, 2018