How do you simplify (4x+2)/(5x) + (10x-1)/(20x) + (2x-3)/(4x)4x+25x+10x−120x+2x−34x?
1 Answer
Explanation:
Your goal here is to find the common denominator for all those fractions and multiply each one so that you can get them to have the same denominator.
This will in turn allow you to add the resulting numerators and simplify the expression.
So, your three denominators are
5 * x" "5⋅x ," "20 * x" " 20⋅x , and" "4 * x 4⋅x
Notice that you can rewrite
20x = 5 * 4 * x20x=5⋅4⋅x
This means that you can use this as the common denominator for the three fractions, and multiply the first one by
The expression can thus be written as
(4x+2)/(5x) * 4/4 + (10x-1)/(20x) + (2x-3)/(4x) * 5/54x+25x⋅44+10x−120x+2x−34x⋅55
((4x + 2) * 4)/(20x) + (10x-1)/(20x) + ((2x-3) * 5)/(20x)(4x+2)⋅420x+10x−120x+(2x−3)⋅520x
Now that the fractions have the same denominator, add the numerators like you normally would
(4x + 2) * 4 + 10x - 1 + (2x-3) * 5(4x+2)⋅4+10x−1+(2x−3)⋅5
16x + 8 + 10x - 1 + 10x - 1516x+8+10x−1+10x−15
36x - 8 = 4 * (9x-2)36x−8=4⋅(9x−2)
The expression can be simplified to
(color(red)(cancel(color(black)(4))) * (9x-2))/(color(red)(cancel(color(black)(4))) * 5x) = color(green)( (9x-2)/(5x))
