SOLUTION: me and my aunt keep getting different answers. this is weekend homework. Multiply or divide. Simplify. 1) ((x^2-9)/(x^2-4x))*((2x-8)/(x+3)) 2) (m^2+10m+25m)/(m^2+12m+35)

Algebra ->  Expressions -> SOLUTION: me and my aunt keep getting different answers. this is weekend homework. Multiply or divide. Simplify. 1) ((x^2-9)/(x^2-4x))*((2x-8)/(x+3)) 2) (m^2+10m+25m)/(m^2+12m+35)       Log On


   

Question 154277: me and my aunt keep getting different answers. this is weekend homework.
Multiply or divide. Simplify.
1) ((x^2-9)/(x^2-4x))*((2x-8)/(x+3))
2) (m^2+10m+25m)/(m^2+12m+35)
3) ((y^2+4y+4)/(y^2+3y+2))/((y^2+6y+8)/(y^2+4y+3))

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started:

# 1


%28%28x%5E2-9%29%2F%28x%5E2-4x%29%29%28%282x-8%29%2F%28x%2B3%29%29 Start with the given expression.


%28%28%28x-3%29%28x%2B3%29%29%2F%28x%5E2-4x%29%29%28%282x-8%29%2F%28x%2B3%29%29 Factor x%5E2-9 to get %28x-3%29%2A%28x%2B3%29.


%28%28%28x-3%29%28x%2B3%29%29%2F%28x%28x-4%29%29%29%28%282x-8%29%2F%28x%2B3%29%29 Factor x%5E2-4x to get x%2A%28x-4%29.


%28%28%28x-3%29%28x%2B3%29%29%2F%28x%28x-4%29%29%29%28%282%28x-4%29%29%2F%28x%2B3%29%29 Factor 2x-8 to get 2%28x-4%29.


%282%28x-3%29%28x%2B3%29%28x-4%29%29%2F%28x%28x-4%29%28x%2B3%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


%282%28x-3%29%29%2F%28x%29 Simplify.


%282x-6%29%2F%28x%29 Distribute


So %28%28x%5E2-9%29%2F%28x%5E2-4x%29%29%28%282x-8%29%2F%28x%2B3%29%29 simplifies to %282x-6%29%2F%28x%29.


In other words, %28%28x%5E2-9%29%2F%28x%5E2-4x%29%29%28%282x-8%29%2F%28x%2B3%29%29=%282x-6%29%2F%28x%29 where x%3C%3E-3, x%3C%3E0, or x%3C%3E4




# 2

I'm assuming that you meant to say %28m%5E2%2B10m%2B25%29%2F%28m%5E2%2B12m%2B35%29


%28m%5E2%2B10m%2B25%29%2F%28m%5E2%2B12m%2B35%29 Start with the given expression.


%28%28m%2B5%29%28m%2B5%29%29%2F%28m%5E2%2B12m%2B35%29 Factor m%5E2%2B10m%2B25 to get %28m%2B5%29%28m%2B5%29.


%28%28m%2B5%29%28m%2B5%29%29%2F%28%28m%2B7%29%2A%28m%2B5%29%29 Factor m%5E2%2B12m%2B35 to get %28m%2B7%29%2A%28m%2B5%29.


%28highlight%28%28m%2B5%29%29%28m%2B5%29%29%2F%28%28m%2B7%29highlight%28%28m%2B5%29%29%29 Highlight the common terms.


%28cross%28%28m%2B5%29%29%28m%2B5%29%29%2F%28%28m%2B7%29cross%28%28m%2B5%29%29%29 Cancel out the common terms.


%28m%2B5%29%2F%28m%2B7%29 Simplify.


So %28m%5E2%2B10m%2B25%29%2F%28m%5E2%2B12m%2B35%29 simplifies to %28m%2B5%29%2F%28m%2B7%29.


In other words, %28m%5E2%2B10m%2B25%29%2F%28m%5E2%2B12m%2B35%29=%28m%2B5%29%2F%28m%2B7%29 where m%3C%3E-7 or m%3C%3E-5