Adding Rational Expressions

[PinkGlasses]

I need help adding d² - 9d + 20/ d² - 3d -10 and d² - 2d-8 / d² +4d -32


I know the answer is 2d² + 8d - 28/ (d+2)(d+8), but I'm having trouble arriving at that answer. Here's what I've done so far.


(d² - 9d + 20) / ( d² - 3d -10) + (d² - 2d-8)/ (d² +4d -32)







(d² - 9d + 20)/(d+2)(d-5) + ( d² - 2d-8)/ (d+8)(d-4)




(d² - 9d + 20)/(d+2)(d-5) x (d+8)(d-4)/(d+8)(d-4) + ( d² - 2d-8)/ (d+8)(d-4) x (d+2)(d-5) /(d+2)(d-5)


(d² - 9d + 20)(d+8)(d-4) +( d² - 2d-8)(d+2)(d-5) /(d+2)(d-5) (d+8)(d-4)

 

[MarkFL]

Factor the numerators too, and then you will be able to simplify the addends by dividing out common factors.

 

[PinkGlasses]

Sorry I'm late replying, but thank you for the help! I had spent at least an hour earlier trying to figure out what I did wrong so I'm grateful I finally know what my mistake was.

 

[Deleted member 4993]

I need help adding d² - 9d + 20/ d² - 3d -10 and d² - 2d-8 / d² +4d -32


I know the answer is 2d² + 8d - 28/ (d+2)(d+8), but I'm having trouble arriving at that answer. Here's what I've done so far.


(d² - 9d + 20) / ( d² - 3d -10) + (d² - 2d-8)/ (d² +4d -32)

(d² - 9d + 20)/(d+2)(d-5) + ( d² - 2d-8)/ (d+8)(d-4)

(d² - 9d + 20)/(d+2)(d-5) x (d+8)(d-4)/(d+8)(d-4) + ( d² - 2d-8)/ (d+8)(d-4) x (d+2)(d-5) /(d+2)(d-5)

(d² - 9d + 20)(d+8)(d-4) +( d² - 2d-8)(d+2)(d-5) /(d+2)(d-5) (d+8)(d-4)

(d² - 9d + 20) /( d² - 3d -10) + (d² - 2d-8)/(d² +4d -32)

= [(d-5)(d-4)]/[(d-5)(d+2)] + [(d-4)(d+2)]/[(d+8)(d-4)]

= (d-4)/(d+2) + (d+2)/(d+8)

=[(d+8)(d-4) + (d+2)(d+2)]/[(d+2)(d+8)]

=(d² + 4d - 32 + d² + 4d + 4)/[(d+2)(d+8)]

= (2d² + 8d - 28)/[(d+2)(d+8)]

= 2(d² + 8d - 14)/[(d+2)(d+8)]