3/2y-3/2y+4
=
rational expression reduce to lcd
The way you typed it ....
3/2y-3/2y+4
= 4
If you meant ....
3/(2y-3) - 3/(2y+4) then
= (3(2y+4) - 3(2y-3))/((2y-3)(2y+4))
= (6y+12-6y+9)/((2y-3)(2y+4))
= 21/((2y-3)(2y+4))
3/(2y) - 3/(2y+4)
= [3(2y+4) -3(2y]/[(2y)(2y+4)]
= [6y +12 -6y]/[(2y)(2y+4)]
= 12/[(2y)(2y+4)]
I interpreted your problem differently from Reiny due to the ambiguous lack of parentheses.
To reduce the given rational expression to its simplest form, we need to find the least common denominator (LCD) and then simplify the expression using it. Here's how you can do it step by step:
Step 1: Identify the denominators
In the given expression, the denominators are "2y" and "2y+4".
Step 2: Find the LCD
To find the LCD, we need to factor each denominator and take the highest power of each factor.
For "2y", the factors are 2 and y, and the highest power of each factor is 1. So, the factorization of "2y" is 2 * y.
For "2y+4", we can factor out the common factor of 2, which gives us 2(y+2).
Since we have two distinct factors (2 and y+2), the LCD is the product of these factors: 2 * (y+2) = 2(y+2).
Step 3: Adjust the expression with the LCD
To adjust the expression with the LCD, multiply each term of the expression by the factors that are needed to make the denominators equal to the LCD.
For the term "3/2y", we need to multiply both numerator and denominator by (y+2), which gives us (3(y+2))/(2y(y+2)).
For the term "-3/2y+4", we already have the denominator as "2(y+2)" which is the LCD.
Step 4: Simplify the expression
Now that we have adjusted the expression using the LCD, we can simplify it further. Combine the numerators and leave the denominator as it is.
The adjusted expression becomes: (3(y+2) - 3)/ (2y(y+2)).
Simplifying further, we have: (3y + 6 - 3) / (2y(y+2))
Simplifying the numerator: (3y + 3) / (2y(y+2))
And that's the simplest form of the given rational expression after reducing it to the least common denominator (LCD).