Question

[1/1+6] + [3/x+4] = -2 / x^2+10x+24

Answer 1

kathy, something is missing, is it [1/1+6x]?

Answer 2

sorry , 1 / x+6

Answer 3

ok :)

Answer 4

Again find what are the denominator for each of the fractions.

Answer 5

on the left hand side, you have x+6 and x+4. What do you have on the right side?

Answer 6

x^2+ 10 + 24 = (x+6)(x+4)

Answer 7

but how do i put the other together to make the same

Answer 8

great kathy. So we only have z+6 and z+4 in the denominator. On the right side, we don't have to do anything. For the left side, make each fractions to have (x+6)(x+4) as denominator. Then compare the numerator

Answer 9

oops...typo..x+6 and x+4

Answer 10

[1/x+6] + [3/x+4] = -2 / x^2+10x+24
[(x+4)/(x+6)(x+4)] + [3(x+6)/(x+4)(x+6)] = -2 /(x+6)(x+4)

Answer 11

hmmm i dont get it, we dont have to make the left side denominator the same as the right ?

Answer 12

oh i see, but what do i do after?

Answer 13

compare the numerator, because now you already have the denominator to be the same. The idea is just the same when we deal with number. I hope the following illustration with numbers can help you:

1/2 + 1/4 = y/24
12/24 + 6/24 = y/24
-> 12 + 6 = y

Answer 14

oh so now i just add : x+4 +3(x+6) = -2

Answer 15

/ (x+6)(x+4)

Answer 16

yup, you are right kathy. well done!

Answer 17

[x+4 +3(x+6)]/(x+6)(x+4) = -2/(x+6)(x+4)

by comparing the numerator, you get

x+4 +3(x+6) = -2

Answer 18

4x+22=-2/ (x+6)(x+4)

Answer 19

no need the / (x+6)(x+4)

Answer 20

so it cancels out ?

Answer 21

x=5

Answer 22

but what happens to the denominator

Answer 23

I wont say cancel out, I would rather say for the left and right to be equal and since the denominators are same, then the numerator must be the same

Answer 24

[x+4 +3(x+6)]/(x+6)(x+4) = -2/(x+6)(x+4)
by comparing the numerator, you get
x+4 +3(x+6) = -2

Answer 25

which equals to : 4x + 22 = -2
4x = 20
x=5

Answer 26

4x + 22 = -2
4x = -24
x = -6

Answer 27

my mistake. so after that what would happen to the denominator so we can find x

Answer 28

well, the original equation is
[1/x+6] + [3/x+4] = -2 / x^2+10x+24

from this we know that our solution x cannot be -6 or -4. So as a conclusion, i will say there is no solution for this problem, even though we solve to get x = -6

Answer 29

Does it make sense to you?

Answer 30

true,
so it has no answer ?

Answer 31

ya, there is no answer for this problem

Answer 32

1/2t + 6/t =1
1/2t + 12/2t =13/2t
13/2t = 1
divide both by 2 to leave x alone & its 13/2

Answer 33

just doube checking this other problem

Answer 34

or is it 7/2

Answer 35

are you still there?