Question

I am stuck on a complex rational problem
solve, simplify result. leave in factored form

x-2/x+2 + x-1/x+1 / x/x+1 - 2x-3/x

Answer 1

please help

Answer 2

\[\frac{x-2}{x+2} + \frac{x-1}{x+1 }\div (\frac{x}{x+1} - \frac{2x-3}{x})\]

Answer 3

yeah that is the problem, thank you

Answer 4

is that it? hard to read

Answer 5

holy crap. your math teacher must really hate you.

Answer 6

i was trying to type it the way you do but i don't i can't find a way to write it with the equation tool

Answer 7

i do not see a snap way to do this, so you are going to have to add the first two terms, subtract the last two and then invert and multiply. i guess we just have to grind it out

Answer 8

ready?

Answer 9

yeah

Answer 10

ok first
\[\frac{x-2}{x+2}+\frac{x-1}{x+1}=\frac{(x-2)(x+1)+(x+2)(x-1)}{(x+2)(x+1)}\]

Answer 11

lets leave denominator in factored form. numerator is
\[x^2-x-2+x^2+x-2=2x^2\]
so we have for the first part
\[\frac{2x^2}{(x+2)(x+1)}\]

Answer 12

ok i follow

Answer 13

now
\[\frac{x}{x+1}-\frac{2x-3}{x}\]
\[=\frac{x^2-(2x-3)(x+1)}{x(x+1)}\]

Answer 14

again we leave denominator in factored form and multiply out in the top
\[x^2-(2x^2-x-3)=x^2-2x^2+x+3=-x^2+x+3\]

Answer 15

you should check my algebra but i think it is right. so second part is
\[\frac{-x^2+x+3}{x(x+1)}\]

Answer 16

i am trying to see where the \[x^{2}\] came from

Answer 17

\[\frac{a}{b}-\frac{c}{d}=\frac{ac-bd}{bd}\] and here both a and c are x

Answer 18

i mean both a and d are x

Answer 19

still not done. now we have to invert and multiply

Answer 20

ok i see

Answer 21

\[\frac{2x^2}{(x+2)(x+1)}\times \frac{x(x+1)}{-x^2+x+3}\]

Answer 22

you can cancel a factor of x+1 from top and bottom
that is about it. unless i made some other mistake.

Answer 23

i get
\[\frac{2x^3}{(x+2)(-x^2+x+3)}\]

Answer 24

check my algebra, but i think it is right. the method is certainly right

Answer 25

the back of my book , shows -2x^2(x^2-2) for the top part. maybe my book is wrong

Answer 26

it is entirely possible that i made a mistake somewhere.

Answer 27

there is a mistake in the first fraction. it should come out to \[2x ^{2}-4\]--------
(x+2)(x+1)

Answer 28

how do you like that ! you are right. it is
\[x^2-4\] for the first one