Divide. Simplify your answer.
1. 3a^4b/2a^2c^3 ÷ 12a^2c/8c^4
A: ?
2. x^2 + 4x - 5/3x - 3 ÷ (xC^2 - 25)
A: ?
To simplify these division problems, we will follow these steps:
Step 1: Factorize the expressions, if possible.
Step 2: Cancel out common factors in the numerator and denominator.
Step 3: Divide the remaining terms.
Let's apply these steps to each problem:
1. 3a^4b/2a^2c^3 ÷ 12a^2c/8c^4
Step 1:
Factorize the expressions:
3a^4b/2a^2c^3 = (3 * a * a * a * a * b) / (2 * a * a * c * c * c)
12a^2c/8c^4 = (12 * a * a * c) / (8 * c * c * c * c)
Step 2:
Cancel out common factors:
In the numerator, we have 3 * a * a * a * b, and in the denominator, we have 2 * a * a * c.
Cancelling a, a, and b, the expression becomes:
(3 * a)/(2 * c^2)
Step 3:
We divide the remaining terms:
3 * a divided by 2 * c^2 is equal to (3a)/(2c^2).
2. (x^2 + 4x - 5)/(3x - 3) ÷ (x^2 - 25)
Step 1:
Factorize the expressions:
(x^2 + 4x - 5)/(3x - 3) = ((x - 1)(x + 5))/(3(x - 1))
(x^2 - 25) = (x - 5)(x + 5)
Step 2:
Cancel out common factors:
In the numerator, we have (x - 1)(x + 5), and in the denominator, we have 3(x - 1) and (x - 5)(x + 5).
Cancelling (x - 1) and (x + 5), the expression becomes:
1/(3 * (x - 5))
Step 3:
We divide the remaining terms:
1 divided by (3 * (x - 5)) is equal to 1/(3(x - 5)).
Therefore, the simplified answers are:
1. (3a)/(2c^2)
2. 1/(3(x - 5))
when dividing by a fraction, just invert and multiply. So,
#1
3a^4b/2a^2c^3 * 8c^4/12a^2c
= 3*8/12 a^4/a^2 b c/c^3
...
#2
x^2+4x-5 = (x+5)(x-1)
x^2-25 = (x+5)(x-5)
So, you just have
(x+5)(x-1) / 3(x-1) * 1 / (x+5)(x-5)
= (x+5)(x-1) / 3(x+5)(x-1)(x-5)
= ...
1. A: ?
2. A: 1/3x-15
Am I correct?
I still don't know the answer to #1.
Hmmm. How about
2a^2b / c^2
Is this the answer to #1? Or am I incorrect?
yes,
#1 = 2a^2b/c^2
#2 = 1/(3x-15)