Question

simplify each rational expresion

Answer 1

\[\frac{ 3 }{ x^{3} +3x -10} + \frac{1 }{ x^{2}+6x +5 }\]

Answer 2

Factor the denominator

Answer 3

can you help i have final test tomorrow

Answer 4

ill give medal and became fan

Answer 5

I am trying to help.. but you need to follow along.. so can you factor the denominators?

Answer 6

I gtg but I'm sure @whpalmer4 @tHe_FiZiCx99 or @zepdrix can help if you need it..

Answer 7

Lui I was getting off myself >.>

Answer 8

help me plz

Answer 9

lol is that a leopard mustache? :x

Answer 10

yes :D

Answer 11

HAHAHA

Answer 12

So we have to simplify this?
\[\Large\bf\sf \frac{3}{x^{3}+3x-10}+\frac{1}{x^{2}+6x +5}\]You sure the first one isn't a square on bottom?

Answer 13

can you help me plz i need a procedure to studdy for my test tomorrow

Answer 14

yes!!!

Answer 15

yes you're sure? :o
i'm confused..

Answer 16

Because this problem would make a lot more sense,\[\Large\bf\sf \frac{3}{x^{2}+3x-10}+\frac{1}{x^{2}+6x +5}\]

Answer 17

yyeah i know to simplify

Answer 18

Do you know how to factor this?
\[\Large\bf\sf x^2+3x-10\]

Answer 19

idk if my teacher got confused but lets do it that way

Answer 20

yes wait!! plz

Answer 21

ya teach musta got confused D:
we cant actually simplify it if it's the other way.

Answer 22

For -10?
Hmm I think we need 5 and 2, yes?

Answer 23

5 ans -2

Answer 24

\[\Large\bf\sf \frac{3}{(x+5)(x-2)}+\frac{1}{x^{2}+6x +5}\]Ok good! How bout the other one? :U

Answer 25

i think ther is nor number

Answer 26

sorry
5 and 1

Answer 27

Ok great!\[\Large\bf\sf \frac{3}{(x+5)(x-2)}+\frac{1}{(x+5)(x+1)}\]So now we must combine the fractions.
To do so, we need a common denominator.

Answer 28

\[\Large\bf\sf \frac{3}{\color{orangered}{(x+5)}(x-2)}+\frac{1}{\color{orangered}{(x+5)}(x+1)}\]Both fractions share a common factor.
So we don't need to worry about that one.

Answer 29

The first fraction is missing a factor of (x+1)
while the second fraction is missing a factor of (x-2)

Answer 30

my teacher told me to combiine common and not common :( soo will be (xplus5)(x-2)(xplus1) i think idk

Answer 31

Yes that will be the common denominator,
The (x+5) that they both share,
and the (x-2) and (x+1).

But to `get` that common denominator, we need to give the first fraction (x+1) in the top and bottom.

Answer 32

\[\Large\bf\sf \frac{3\color{royalblue}{(x+1)}}{(x+5)(x-2)\color{royalblue}{(x+1)}}+\frac{1}{(x+5)(x+1)}\]

Answer 33

And the second fraction needs a factor of (x-2) in the top and bottom.\[\Large\bf\sf \frac{3(x+1)}{(x+5)(x-2)(x+1)}+\frac{1\color{royalblue}{(x-2)}}{(x+5)\color{royalblue}{(x-2)}(x+1)}\]

Answer 34

Understand what I did there?
They have the same denominator now.

Answer 35

yeah but why you just multiply the x plus 1 and not the others ones

Answer 36

ohhh oh i get it

Answer 37

\[\Large\bf\sf \frac{3(x+1)}{(x+5)(x-2)(x+1)}+\frac{\color{orangered}{1(x-2)}}{(x+5)(x-2)(x+1)}\]
Since they have the same denominator,
you can write it as one fraction now,\[\Large\bf\sf \frac{3(x+1)+\color{orangered}{1(x-2)}}{(x+5)(x-2)(x+1)}\]

Answer 38

yeah i did that on my notebook

Answer 39

Ok good.
From there, multiply out the brackets in the `numerator`, and combine like-terms.

Answer 40

you cant cancel right?

Answer 41

No there won't be any cancelling we can do.

Answer 42

and the (xplus1) and (x-2)

Answer 43

so the final result will be?

Answer 44

idk if i got

Answer 45

right

Answer 46

When you distribute the 3 to each term in the brackets,
And the 1 to each term in the second set of brackets,
the numerator becomes,\[\Large\bf\sf 3x+3+x-2\]Then combining like terms gives us a final answer of,\[\Large\bf\sf \frac{4x+1}{(x+5)(x-2)(x+1)}\]

Answer 47

oh thx so much doest it bother if you can help with complex fractions

Answer 48

Sorry I need a math break >:U
Had a bad test day today grr..

Answer 49

oh so sorry I have my test tomorrow :( but htnak you help me a lot