Algebraic Multiplication?

Question

(3a + 9) / (2a - 6) Multiplied by (4a + 4) / (a + 3)

Answer 1

Algebraic rules say you can multiply the numerator and denomiator separately. First, the numerators:
(3a+9)(4a+4) = (12a^2+36a+12a+36) = 12a^2+48a+36

Now, the denominators:
(2a-6)(a+3) = (2a^2-6a+6a-18) = 2a^2-18

If you put them back in, you get:
(12a^2+48a+36) / (2a^2-18)

To simplify, you can multiply the numerator and denominator by 1/2 to get:
(6a^2+24a+18) / (a^2-9)

There's too much to type for the algebraic separation of hte fraction, but what you do is separate the numerator's terms with the common denomiator of (a^2-9). Simplify each expression, and the final answer is:

(6a+6) / (a-3)

Answer 2

[ 2a-6 and a+3 must not be 0
so a should be different from -3]


(3a+9)(4a+4) = 12* a in the second + 12a+ 36a + 36 = 12* a in the second +48a + 36

(2a - 6)(a+3) = 2* a in the second + 6a -6a - 18 = 2* a in the second - 18

so, alltogether it is:
(12* a in the second + 48a + 36)/(2* a in the second - 18) =
2(6 * a in the second + 24a + 18)/2(a in the second - 9)=
(6 * a in the second + 24a +18)/(a in the second - 9)


6*a in the second + 24a+ 18
Δ= 24*24 -4*6*18 = 144
α= (-24 + - 12)/ 2*6
α= -3 OR α= -1

the case when a= -3 is not allowed by the restrictions,
so, a= -1 and
(6 * a in the second + 24a +18)/(a in the second - 9) =
(6*1 + 18 - 24)/(1 - 9) = 0/-8 = 0

Answer 3

Factor a 3 out of 3a+9, so it is 3(a+3)
Factor a 2 out of 2a-6, so it is 2(a-3)
Factor a 4 out of 4a+4, so it is 4(a+1)

3(a+3)/2(a-3) x 4(a+1)/a+3
After you cancel out terms it's 3/2(a-3) x 4(a+1)
So it is 12(a+1)/2(a-3)
But you can also get ride of the 2, so it's 6(a+1)/(a-3)
So the answer is 6a+6/a-3
I hope I factor out right. (:

Answer 4

3(a+3)/2(a-3) * 4(a+1)/ a+3 eliminate the 2 a+3
3/2(a-3)*4(a+1) make the 2 a one and the 4 a two
3/a-3*4(a+1)=
12(a+1)/2( a-3)=
6(a+1)/a-3

Answer 5

6x^3-6x^2/ x^4+5x^3 * 2x^2+2x-40/ 3x^2-15x+12 x/x^3(x+5) * (2x-8)(x+5)/(3x-3)(x-4) x 2(x-4)(x+5) ------- * -------------------------- x^3(x+5) (3x-3)(x-4) 2/x^2(3x-3)=2/6x^3-6x^2=2/x--answer