SOLUTION: I need help Subtracting Rational Expressions with different Denominators. I'm missing one step, but can't figure it out! Ex. problem 4y-1 y+3

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Question 35577This question is from textbook Introductory Algebra
: I need help Subtracting Rational Expressions with different Denominators. I'm missing one step, but can't figure it out!
Ex. problem
4y-1 y+3
_________ - __________
2y^2+5y-3 6y^2+y-2 This question is from textbook Introductory Algebra

Answer by stanbon(48564) (Show Source):
You can put this solution on YOUR website!

[4y-1]/[2y^2+5y-3] - [y+3]/[6y^2+y-2]
Factor where you can as follows:
[4y-1]/[(2y-1)(y+3)]-[y+3]/[(2y-1)(3y+2)]
The LCD = (2y-1)(y+3)(3y+2)
Rewrite each fraction over the LCD, as follows:
[(4y-1)(3y+2)]/LCD - [(y+3)(y+3)]/LCD
Simplify:
[12y^2+5y-1-(y^2+6y+9)]/LCD
[11y^2-y-10]/LCD
[(11y+10)(y-1)]/LCD
Cheers,
stan H.