[2x-12]/[3x-6] * [x^2-4]/[x^2-36] * [3x+18]/[4x+8]
Would it be x+4 over 2(x+2)(x-2)?
yea
To simplify the expression:
Step 1: Factorize the numerator and denominator expressions separately.
Numerator 1: 2x - 12 = 2(x - 6)
Denominator 1: 3x - 6 = 3(x - 2)
Numerator 2: x^2 - 4 = (x + 2)(x - 2)
Denominator 2: x^2 - 36 = (x + 6)(x - 6)
Numerator 3: 3x + 18 = 3(x + 6)
Denominator 3: 4x + 8 = 4(x + 2)
Step 2: Cancel out common factors between the numerators and denominators.
Cancel out (x - 2) in Numerator 1 and Denominator 1:
2(x - 6) / 3(x - 2) = 2/3
Cancel out (x + 6) in Numerator 2 and Denominator 2:
(x + 2)(x - 2) / (x + 6)(x - 6) = (x + 2)/(x - 6)
Cancel out (x + 2) in Numerator 2 and Denominator 3:
(x + 2)3(x + 6) / (x - 6)4(x + 2) = 3(x + 6) / 4(x - 6)
Step 3: Combine the simplified expressions.
2/3 * (x + 2)/(x - 6) * 3(x + 6) / 4(x - 6)
Multiply the numerators together:
2 * (x + 2) * 3(x + 6) = 6(x + 2)(x + 6)
Multiply the denominators together:
3 * 4 * (x - 6)(x - 6) = 12(x - 6)^2
Combine the simplified expressions:
[6(x + 2)(x + 6)] / [12(x - 6)^2]
Now, let's further simplify the expression:
Step 4: Divide the numerator and denominator by their greatest common divisor (GCD), which is 6:
[6(x + 2)(x + 6)] / [12(x - 6)^2] = [(x + 2)(x + 6)] / [2(x - 6)^2]
Therefore, the simplified expression is (x + 2)(x + 6) / 2(x - 6)^2.
So, the answer is not x + 4 over 2(x + 2)(x - 2), but rather (x + 2)(x + 6) / 2(x - 6)^2.