How do I reduce this fraction:
-6 - 18x / 6x + 2
-6(3x+1)
-----------
2 (3x+1)
= -3
First divide the entire equation by 2. That gives you the fraction -3-9x/3x+1. Then, divide the top part of the fraction by the bottom part which will give you a final answer of -3.
Factor the numerator and factor the denominator.
Then cancel like factors. Which is 3x + 1
Note, you removed the -6 so that the terms in your factor will be positive and match the denominator's factor.
To reduce a fraction, you need to find the greatest common factor (GCF) of the numerator and denominator, and then divide both the numerator and denominator by the GCF.
In this case, the numerator is -6 - 18x and the denominator is 6x + 2.
First, let's simplify the numerator -6 - 18x:
-6 - 18x = -6(1 + 3x)
Next, let's simplify the denominator 6x + 2:
6x + 2 = 2(3x + 1)
Now, we can rewrite the fraction as:
(-6)(1 + 3x) / 2(3x + 1)
The GCF of -6 and 2 is 2, and the GCF of (1 + 3x) and (3x + 1) is 1. Therefore, we can divide the numerator and denominator by the GCF, which is 2:
((-6)(1 + 3x) / 2(3x + 1)) / 2
Simplifying further:
(-3)(1 + 3x) / (3x + 1)
Therefore, the fraction (-6 - 18x) / (6x + 2) can be simplified to (-3)(1 + 3x) / (3x + 1).