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

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

Mathematics
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kathy, something is missing, is it [1/1+6x]?
sorry , 1 / x+6
ok :)

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Other answers:

Again find what are the denominator for each of the fractions.
on the left hand side, you have x+6 and x+4. What do you have on the right side?
x^2+ 10 + 24 = (x+6)(x+4)
but how do i put the other together to make the same
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
oops...typo..x+6 and x+4
[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)
hmmm i dont get it, we dont have to make the left side denominator the same as the right ?
oh i see, but what do i do after?
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
oh so now i just add : x+4 +3(x+6) = -2
/ (x+6)(x+4)
yup, you are right kathy. well done!
[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
4x+22=-2/ (x+6)(x+4)
no need the / (x+6)(x+4)
so it cancels out ?
x=5
but what happens to the denominator
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
[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
which equals to : 4x + 22 = -2 4x = 20 x=5
4x + 22 = -2 4x = -24 x = -6
my mistake. so after that what would happen to the denominator so we can find x
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
Does it make sense to you?
true, so it has no answer ?
ya, there is no answer for this problem
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
just doube checking this other problem
or is it 7/2
are you still there?

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