Question

Algebra II help: Rational equations (question in comment)

Answer 1

\[\frac{ 4 }{ x-1 }+\frac{ 7 }{ x }=9\]

Answer 2

Step one, get the x's out of the denom. \[4x+7(x-1)=9x(x-1)\]

Answer 3

4x+7x-7=9x^2-9

Answer 4

now, x's to one side, numbers to the other

Answer 5

wait! it's a quadratic, everything to one side.

Answer 6

\[9x^2-20x+7\]

Answer 7

-11x?

Answer 8

no -20x... I messed up the first equation... it's 4x+7x-7=9x^2-9x

Answer 9

oh, ok ---> looks like quadratic formula time

Answer 10

\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 11

I get \[x= \text{stuff} + \frac{\sqrt{37}}{\text{other stuff}}\]

Answer 12

idk that's where I get so lost

Answer 13

\[\frac{ -(-20)\sqrt{20^2-2(9)(7)} }{ 2(9) }\]

Answer 14

we have a=9,b=-20,c=7... so \[x=\frac{20\pm\sqrt{20^2-4(9)(7)}}{2(9)}\]

Answer 15

I agree

Answer 16

okay sooo....\[\frac{ 20\pm \sqrt{400-252} }{ 18}\]

Answer 17

yep. but it might be easier to leave the denom. as 2*9

Answer 18

why?

Answer 19

to reduce the answer latter.. it's not important, just saves a step

Answer 20

*later

Answer 21

okay so now what?

Answer 22

lets work inside the root: 400-252=148

Answer 23

right... so now it's \[\frac{ 20\pm \sqrt{148} }{ 2*9 }\]

Answer 24

yep, it's done but reducing...

\[2^2*37=148\]... so \[\sqrt{2^2*37}=2\sqrt{37}\]

Answer 25

and lets also try and factor a two out of twenty, since we have one in the second term.

Answer 26

so that's the final answer?

Answer 27

oh ok

Answer 28

almost... its a good answer but can be written to look better.

Answer 29

I'm confused... where does the 20 come from?

Answer 30

oh, ignore that line, it's stated confusingly... atm we have\[x=\frac{20\pm 2\sqrt{37}}{2*9}\], correct?

Answer 31

yes

Answer 32

ok, can we simplify more?

Answer 33

somehow...

Answer 34

\[\frac{ 10 \pm1\sqrt{37} }{ 9 }\]

Answer 35

yep! \[x=\frac{10}{9}\pm\frac{\sqrt{37}}{9}\]

Answer 36

ah I see, thank you <3

Answer 37

np. :)