Question

Solve rational equations (k-2)/(k+1) =(7k+22)/(k^2+6k+5)

Answer 1

cross multiply and simplify.

Answer 2

Don't you use the quadratic formula?

Answer 3

Well, you can solve this a couple of ways.
You can factor the (k^2+6k+5) first and see if any factor cancels out.
Let us try that approach.
What are the factors of (k^2+6k+5)?

Answer 4

k+5 and k+1

Answer 5

Exactly! So the (k+1) in the denominator on the right cancels out with the (k + 1) in the denominator of the left. Now you can simplify.

Answer 6

Im stuck with the 7k+22

Answer 7

Im suppose to get the answer k=-4 and k=8

Answer 8

(k-2)/(k+1) = (7k+22)/(k^2+6k+5)
(k-2)/(k+1) = (7k+22)/((k+5)(k+1))
(k+1) cancels out.
(k-2) = (7k+22)/(k+5)
cross multiply
(k-2) * (k + 5) = 7k + 22
k^2 + 5k - 2k - 10 = 7k + 22
k^2 + 3k - 10 - 7k - 22 = 0
k^2 - 4k - 32 = 0
factor and solve for k.

Answer 9

Thanks for typing all of that!
Then you can use the quadratic equation?

Answer 10

You can use the quadratic equation. But my preference is to always try to see if I can factor it.
k^2 - 4k - 32 = 0
write it as:
k^2 - 8k + 4k - 32 = 0
k(k - 8) + 4(k - 8) = 0
(k + 4)(k - 8) = 0
k = -4 or 8

Answer 11

I see! It would be faster with factoring now! Thank you so much for walking me through this!

Answer 12

You are welcome.

BTW, I answered your other question with long division although it is closed now.

Answer 13

Oh! HA! I figured it out! Thank you

Answer 14

I do have another one that Im going to post.

Answer 15

f(x)=\[\sqrt[7]{x+20?}\] a. find f(-60) b. f(x) =-3

Answer 16

For f(-60) you just need to put x = -60 into the function and evaluate.

Answer 17

I did that but got stuck with the 7. Im going over my notes now to try and figure it out.

Answer 18

the little 7 outside the radical means the seventh root. It is the same as raising it to ^(1/7)

Answer 19

\[\Large f(x) = \sqrt[7]{(x + 20)} = (x + 20)^{\frac{ 1 }{ 7}}\]

Answer 20

Im suppose to have the answer f(-60) aproxi -1.694

Answer 21

Yes. f(x) = (x + 20)^(1/7)
Find f(-60).
Put x = -60
f(-60) = (-60 + 20)^(1/7) = (-40)^(1/7)
Use your calculator to find (-40)^(1/7)
If you don't have a scientific calculator, you can use Google calculator.

Answer 22

The index messes me up.

Answer 23

That is why rewriting the seventh root as exponent (1/7) will make it easier to understand.

Answer 24

I do have a scientific calc and I will check it out. Thank you!

Answer 25

Yes, it does help! Can you do that will all of them?

Answer 26

Yes. BTW, I tried Google calc and I am getting -1.6938

Answer 27

OhhH! I got it1 Yeah!

Answer 28

Alright! Now on to part b.

Answer 29

Are you a professor or you just love math?

Answer 30

Not a prof. Just volunteering cuz it is a good workout for the gray matter and at the same time it gives the satisfaction of helping.

Answer 31

I know how that is... I decided to go back to school after a long time out and Math is my worst subject! But I'm making it. Thank so much for being on here.

B. f(x)=-3

Answer 32

No problem.
f(x) = (x + 20)^(1/7)
f(x) = -3
So we need to solve: -3 = (x + 20)^(1/7)
We need to get rid of the exponent 1/7.
To do that raise both sides to the power of 7. 7 and 1/7 will cancel out on the right.

Answer 33

(-3)^7 = { (x + 20)^(1/7) }^7 = x + 20
(-3)^7 = x + 20
to isolate x, add -20 to both sides:
(-3)^7 - 20 = x
you can use your calc to find (-3)^7 - 20

Answer 34

I am getting x = -2207.

Answer 35

Yes!!! Great thank you! I am now working it out to understand better.

Answer 36

You have have been a huge help!

Answer 37

Glad to be able to assist.
I am leaving this page now. Since it is a closed question the notification may not work to let me know if you had posted any reply or had any question. Even when the question is open the notification is not always timely.

Do well in your math tests. Good luck.

Answer 38

Thank you, I was finished with the questions. Thanks!