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

- anonymous

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

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- anonymous

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

- anonymous

sorry , 1 / x+6

- anonymous

ok :)

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## More answers

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

[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)

- anonymous

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

- anonymous

oh i see, but what do i do after?

- anonymous

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

- anonymous

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

- anonymous

/ (x+6)(x+4)

- anonymous

yup, you are right kathy. well done!

- anonymous

[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

- anonymous

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

- anonymous

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

- anonymous

so it cancels out ?

- anonymous

x=5

- anonymous

but what happens to the denominator

- anonymous

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

- anonymous

[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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Does it make sense to you?

- anonymous

true,
so it has no answer ?

- anonymous

ya, there is no answer for this problem

- anonymous

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

- anonymous

just doube checking this other problem

- anonymous

or is it 7/2

- anonymous

are you still there?

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