Answer:
[tex]\frac{1}{3(x-2)}[/tex]
Step-by-step explanation:
Hi there!
We need to multiply the fractions:
[tex]\frac{x+3}{12x}[/tex]×[tex]\frac{4x}{x^{2}+x-6}[/tex]
Before we multiply, we can cancel out and factor the polynomials to make multiplying easier
First, we can factor x²+x-6
1 (in front of +x) is the sum of two numbers and -6 is the product of those numbers
Those numbers are -2 and 3
so when we factor, we get:
(x-2)(x+3)
here are the fractions so far:
[tex]\frac{x+3}{12x}[/tex]×[tex]\frac{4x}{(x+3)(x-2)}[/tex]
we can cancel out x+3 on both fractions
[tex]\frac{1}{12x}[/tex]×[tex]\frac{4x}{x-2}[/tex]
we can also cancel out 4x from both fractions
[tex]\frac{1}{3}[/tex]×[tex]\frac{1}{x-2}[/tex]
now multiply the fractions together
[tex]\frac{1}{3(x-2)}[/tex]
So the first option is your answer
Hope this helps! :)
