Thread: Simplifying Algebraic Fractions

I've given this a try but I don't think I'm doing it right. If someone could explain what the best way to go about this that would be great. Thanks in advance.

Question (simplify this fraction):
(x/x-2)-(10/(x+3)(x-2))

I tried to get a common denominator and expand out of the brackets but I have a feeling I'm going about this wrong.

I did:

(x^3+x^2-6x+10x-20)/(x^3+x^2-6x-2x^2-2x+12)
(x^3+x^2+4x-20)/(x^3-x^2-8x+12)
(4x-20)/(-8x+12)

However I'm pretty sure I'm doing it wrong.

Thanks!

Originally Posted by hiyarearl

I've given this a try but I don't think I'm doing it right. If someone could explain what the best way to go about this that would be great. Thanks in advance.

Question (simplify this fraction):
(x/x-2)-(10/(x+3)(x-2))

I tried to get a common denominator and expand out of the brackets but I have a feeling I'm going about this wrong.

I did:

(x^3+x^2-6x+10x-20)/(x^3+x^2-6x-2x^2-2x+12)
(x^3+x^2+4x-20)/(x^3-x^2-8x+12)
(4x-20)/(-8x+12)

However I'm pretty sure I'm doing it wrong.

Thanks!

Do some canceling ..

Originally Posted by hiyarearl

I've given this a try but I don't think I'm doing it right. If someone could explain what the best way to go about this that would be great. Thanks in advance.

Question (simplify this fraction):
(x/x-2)-(10/(x+3)(x-2))

I tried to get a common denominator and expand out of the brackets but I have a feeling I'm going about this wrong.

I did:

(x^3+x^2-6x+10x-20)/(x^3+x^2-6x-2x^2-2x+12)
(x^3+x^2+4x-20)/(x^3-x^2-8x+12)
(4x-20)/(-8x+12)

However I'm pretty sure I'm doing it wrong.

Thanks!

Mathaddict, you beat me, but I've added a step at the beginning that might be useful, so I'll post it anyway.



Your common denominator will be

Ah yes of course so:

as when subtracting normal fractions we find the common denominator here effectively we have:



When multiplied by to achieve the common denominator.

I understand now - thank you two very much for your help.

Originally Posted by masters

Mathaddict, you beat me, but I've added a step at the beginning that might be useful, so I'll post it anyway.



Your common denominator will be