SOLUTION: Combine the following rational expressions. (3x+1)/(2x-6) - (x+2)/(x-3)

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Question 906633: Combine the following rational expressions.
(3x+1)/(2x-6) - (x+2)/(x-3)
Found 2 solutions by JoelSchwartz, MathTherapy:
Answer by JoelSchwartz(130)   (Show Source): You can put this solution on YOUR website!
y= the difference between the two numbers
(3x+1)/(2x-6)-(x+2)/(x-3)=y
(2x-6)((3x+1)/(2x-6)-(x+2)/(x-3))=y(2x-6)
3x+1-((x+2)(2x-6))/(x-3)=y(2x+6)
(x+2)(2x-6)=2x^2+4x-6x-12
3x+1-(2x^2+4x-6x-12)/(x-3)=y(2x-6)
(2x^2+4x-6x-12)/(x-3)
2x(x-3)=2x^2-6x
2x^2+4x-6x-12-(2x^2-6x)=4x-12
4(x-3)=4x-12
4x-12-(4x-12)=0
(2x+4)(x-3)=2x^2-2x-12
3x+1-(2x+4)=y(2x-6)
3x+1-2x-4=y(2x-6)
x-3=y(2x-6)
(x-3)/(2x-6)=y
y=(x-3)/2(x-3)
y=1/2
3x+1-(2x+4)=1/2
x-3=1/2
x=3.5
(3*3.5+1)/(2*3.5-6)-(3.5+2)/(3.5-3)=1/2
(11.5)/(1)-(5.5)/(1/2)=1/2
11.5-11=1/2



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Combine the following rational expressions.
(3x+1)/(2x-6) - (x+2)/(x-3)






 ------ Applying LCD, 2(x - 3)





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