SOLUTION: 1. Simplify {(c+3)^2} / (c^2 -9) 2. Simplify (x^2+7x+12)/(x^2-9) 3. Simplify (6y^5)/(24y^3) 4. Multiply and simplify (4a^2/b) * (3b/8a) 5. Multiply and simplify (

Question 184873: 1. Simplify {(c+3)^2} / (c^2 -9)

2. Simplify (x^2+7x+12)/(x^2-9)
3. Simplify (6y^5)/(24y^3)
4. Multiply and simplify (4a^2/b) * (3b/8a)
5. Multiply and simplify (r^2)/(r^2-9) * (r^2 +6r +9)/ (r^2 +3r)
6. {(a^2-1)/(a+1)} * {(2a + 4) / (a^2 +4)/ (a^2 + 5a +6)}

Thanks for your help
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Simplify {(c+3)^2} / (c^2 -9)
= (c+3)^2/[(c-3)(c+3)]
Cancel the common factor of c+3 to get:
=(x+3)/(c-3)
------------------------
2. Simplify (x^2+7x+12)/(x^2-9)
= [(x+3)(x+4)] / [(x-3)(x+3)]
= (x+4)/(x-3)
--------------------------------------
3. Simplify (6y^5)/(24y^3)
= y^2/4
--------------
4. Multiply and simplify (4a^2/b) * (3b/8a)
Calcel common factors: 4, a, b to get
= (a/1)*(3/2)
= (3a/2)
------------------------
5. Multiply and simplify [(r^2)/(r^2-9)] * [(r^2 +6r +9)/ (r^2 +3r)]
= [(r^2)/(r-3)(r+3)] * [(r+3)(r+3)/ r(r+3)]
Cancel common factors: r,(r+3) to get:
= [r/(r-3)] / [1/1]
= r/(r-3)
----------------------------

6. {(a^2-1)/(a+1)} * {(2a + 4) / (a^2 +4)/ (a^2 + 5a +6)}
= [(a-1)/1] * [2(a+2) / (a^2+4)/(a+3)(a+2)]
= [(a-1)/1] * [2 / (a^2+4)/(a+3)]
= [2(a-1) / (a^2+4)(a+3)]
=====================================
Cheers,
Stan H.

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