Would anyone like to take a try at this rational equation problem.?

Question

Show me the steps? thanks
4/7 = 6/c-6 - 8/c-2
Would I start out by finding a common denominator? Would the common denominator be c-42, is c-42 the same as -42c?
Oooooh I am confused.

Answer 1

Your LCD = 7(c - 2)(c - 6)
Multiplying through by this expression you get
(c - 2)(c - 6) = 42(c - 2) - 56(c - 6)
Expanding,
c^2 - 8c + 12 = 42c - 84 - 56c + 336
Gathering like terms,
c^2 + 6c - 240 = 0
c = - 3 ± √(9 + 240)
c = - 3 ± √249

Answer 2

First, you need to clarify the denominators. I'm going to assume that the denominators are 7, c-6, and c-2.
Now that THAT's cleared up, let's solve this!
First, multiply by all the denominators to make life easier.
So: (4/7) * (7)(c-6)(c-2) which = 4(c-6)(c-2)
So: 6/c-6 * (7)(c-6)(c-2) which = 42(c-2)
So: -8/c-2 * (7)(c-6)(c-2) which = -56(c-6)

The result:
4(c-6)(c-2) = 42(c-2) - 56(c-6)

K, now just distribute and solve like a quadratic equation! I'm kinda lazy to actually do it myself right now... but maybe tomorrow morning I'll edit this answer!

Answer 3

4 / 7 = 6 / (c - 6) - 8 / (c - 2)
Multiply both sides by 7 (c - 6) (c - 2) :-
4(c - 6)(c - 2) = 42 (c - 2) - 56 (c - 6)
4(c - 6)(c - 2) = 42c - 56c - 84 + 336
4(c - 6)(c - 2) = 252 - 14c
4(c² - 8c + 12) = 252 - 14c
4c² - 32c + 48 = 252 - 14c
4c² - 18c - 204 = 0
2c² - 9c - 102 = 0
c = [ 9 ± √(81 + 816) ] / 4
c = [ 9 ± √(897) ] / 4 is exact answer
c = 9.74 , c = - 5.24 is approximate answer

Answer 4

LCD is (7)(c-6)(c-2)

so multiply everything you will get:

4(c-6)(c-2) = 42(c-2) - 56(c-6)

4(c^2 -8c +12) = 42c - 84 - 56c +336

4c^2 -32c +12 = -14c + 252

4c^2 - 32c + 48 = -14c +252

4c^2 - 18c - 204 = 0

divide everything by 2

2c^2 - 9c - 102 = 0

n = -b ±√b^2 - 4ac / 2a

c = 9 ±√9^2 - [(4)(2)(-102)] / 2(2)

c = 9 ±√81 +816 / 4

c = 9 ±√897 /4

c = 9 + 29.95 / 4 - uncalculated ans..

c = 38.95/4

c = 9.74- calculated ans

Answer 5

4/7 = 6/c-6 - 8/c-2. put like terms together

4/7 + 6 + 2 = 6/c - 8/c, note sign change, or

4/7 + 8 = -2/c. combine right side

4/7 + 56/7 = -2/c or

60/7 = -2/c. cross multiply

60 c = -2(7) or

60c = -14, so
c = -14/60 or

c = -7/30.