OMG i need help, I'm working on Rational expression: 7- a-2/a+3 = a(squared)-4/a+3 +5.. anyone?

- anonymous

OMG i need help, I'm working on Rational expression: 7- a-2/a+3 = a(squared)-4/a+3 +5.. anyone?

- jamiebookeater

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- anonymous

[7-(a-2/a+3)]=[(a^2-4)/a+3)+5] right?

- anonymous

is it:\[7 - \frac{a-2}{a+3} = \frac{a^2-4}{a+3} + 5\]?

- anonymous

sstarica how you write that symbols

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## More answers

- anonymous

using the equation button down-left on your past box :)

- anonymous

post*

- anonymous

yes that is it!
ok i see the equation button

- anonymous

I did try but I can write the faction

- anonymous

i know the answer but i have no idea how they got it
im so stomped

- anonymous

use frac{}{} for the fraction :), alright, if that's your question then the answer is the following

- anonymous

\[7+5 - \frac{(a-2)}{a+3} - \frac{(a^2-4)}{a+3} = 0\]\[\frac{12(a+3) - a + 2 - a^2 + 4}{a+3} = \frac{12a + 36 - a + 2 - a^2 + 4}{a+3}\]\[= \frac{-a^2-11a+42}{a+3} = \frac{-(a^2+11a-42)}{a+3}\]\[= \frac{-(a+3)(a-14)}{a+3} = -(a-14) \rightarrow -a+14\]
Correct me if I'm wrong ^_^

- anonymous

wait, it's 11 a and not -11 a ^_^" sorry

- anonymous

humm the book has an answer of 4 only, I am confused

- anonymous

so :\[= \frac{-a^2 + 11a +42}{a+3}\]\[= \frac{-(a^2-11a-42)}{a-3} = \frac{-(a+3)(a-14)}{a+3}\]
I just messed up the sign of 11, so in the end when you simplify you'll get -a+14, I guess

- anonymous

4? weird

- anonymous

a = 14 in this case?

- anonymous

yeah, it gives x=4 only

- anonymous

x? but we are dealing with a here

- anonymous

im sorry a
yes

- anonymous

lol, that's weird.

- anonymous

hang on

- anonymous

what i did was mutliply each side by (a+3)

- anonymous

so i ended up with

- anonymous

I GOT IT!

- anonymous

the answer IS 4 lol

- anonymous

steps:

- anonymous

7(a+3) - a - 2 = a^{2}-4 + 5(a+3)

- anonymous

ok show me please..lol

- anonymous

\[\frac{-(a-2)}{a+3} - \frac{a^2-4}{a+3} = 5-7\]\[\frac{-a^2-a-6}{a+3} = -2\]\[\frac{-(a^2+a-6)}{a+3} = -2\]\[\frac{-(a-2)(a+3)}{a+3} = -2\]\[-(a-2) = -2 \rightarrow -a +2 = -2\]\[-a = -4 \rightarrow a = 4\]
^_^

- anonymous

lol in the 2nd line it's supposed to be + 6, but just a small typo, doesn't effect the solution :)

- anonymous

so ur first step was to subtract the entire fraction from one side?

- anonymous

yes, I moved 7 to the other side and got all the a's in one side :) and started solving for a ^_^

- anonymous

oh i didnt know you could do that

- anonymous

lol, it's like solving for x:
4x -3 = x + 2, solve for x <-- move the x's in one side and numbers in one side ^_^

- anonymous

and now since both fractions have the same denominator
i can simply
subtrat the entire top row

- anonymous

yep :)

- anonymous

wait what happend to the (a+3)
how did that cancel?

- anonymous

you simplified, cancel the (a+3) from top and bottom ^_^

- anonymous

and you'll be left with only -(a-2) :)

- anonymous

ok perfect, i got it, then when you divde at the end the two -1's cancel out and -4/-1 = postitive 4.. haha perfect

- anonymous

yep ^_^

- anonymous

next time don't panic :P and face the problem calmly ^_^ good luck!

- anonymous

thank you, it just never crossed my mind that i could move the entire fraction, i was so worried about mutliplying every side the the LCD that i got stuck on it for an hour.. thank you!

- anonymous

my answer: (7*(a+3))-(a-2)=(a^2-4)+(5*(a+3)
(7a+21)-(a-2)=(a^2-4)+(5a+15)
6a+23=a^2+5a+11
a^2-a-12=0
Factor:(a+3)(a-4)

- anonymous

you are most welcome ^_^, worrying = distracts you from concentrating. Look at it as simple as possible then you'll be able to solve it :)

- anonymous

hmm, nancy lam's solution seems simple too :)

- anonymous

nancy ur answer works too i think, its that x would = -3 which would be no solution, but the x=4 would work

- anonymous

but I don't know write like you see better

- anonymous

as long as the denominator isn't zero, from what i remember in class

- anonymous

2 solution , and lug it in to see which one work

- anonymous

i was doing it your way nancy, but somehow, i got messed up with my signs

- anonymous

u got rid of the denominator right from the beginning which is what i was trying to do
im going to work it over again and see where i messed up

- anonymous

I working write fraction like sstarica

- anonymous

you time (a+3) for which one don't have denominator and get rid all denominator from beginning

- anonymous

ok, bye

- anonymous

Thank you, both of you! now i can sleep!

- anonymous

you wellcome

- anonymous

np :)

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