algebra help?

Question

hi eveyone!
i'm kinda having a litle trouble in one of my algebra sums.i'm usualy good in algebra and hardly get any wrong, but recently my teacher has been sick and she didn't explain the hw given so if you could help me in ths one sum ,i could get an example and work the rest of the exercise on my own.

ok so here's the sum,its one of those either or questions.

5/x+3 - 1/x = 1/2


i checked the answer book and the answer is x=2 and/or x=3

if it's possible pleas show the working so i can see how you did it so i may use that method for my hw. it would be even better if you could xplain what you did.

thanks!!!!

Answer 1

5/x + 3 - 1/x = 1/2

2(x + 3)(x)(5/ x + 3) -2(x + 3)(x)(1/x) = 2(x + 3)(x)(1/2)

10x - 2x - 6 = x³ + 3x

8x - 6 = x³ + 3x

8x - 6 = x³ + 3x - 8x

- 6 = x³ - 5x

- 6 + 6 = x³ - 5x + 6

0 = x³ - 5x + 6

The middle term is - 5x

Find the sum of the middle term

first term x = 1

multiply the first them 1 times the last term 6 euals 6 and factor

factors of 6

1 X 6
2 x 3. . . .<=. .use these factors


- 2 and - 3 satisfy the sum of the middle term

since 1 - x

insert - 2x and - 3x into the equation

0 = x³ - 5x - 6

0 = x³ - 2x - 3x- 6

0 = x(x + 2) - 3(x + 2)

0 = (x - 3)(x - 2)
- - - - - - -

Roots

x - 3 = 0

x - 3 + 3 = 0 + 3

x = 3

- - - - - - -

Roots

x - 2 = 0

x - 2 + 2 = 0 + 2

x = 2

- - - - - - -s-

Answer 2

First of all I think the problem is badly written. You have to be accurate in maths. I believe it should be 5/(x+3) - (1/x) = 1/2
then by multiplying the denominators to get the common, we get 2x(x +3) when we multiply the equation throughout we get
2x(x+3)5/(x+3) -2x(x+3)1/x = 1/2 (x+3)2x
10x -2(x+3) = x(x+3)
10x -2x-6 = x^2 + 3x
x^2 -5x + 6 = 0 factorise where the two numbers when multiplied give +6 and when added give -5
(x-2)(x-3) = 0
Hence, either (x-2) = 0 or (x - 3) = 0
x = 2 and x = 3

Answer 3

I think you mean
5/(x+3) - 1/x = 1/2

x cannot be -3 or 0

first this is remove denominator ny mutliplying by 2x(x+3)

10x - 2(x+3) = x(x+3)
or 10 x - 2x - 6 = x^2 + 3x
this is qaudatic so bring all termr to one side
and comibine like terms
x^2 -5x + 6 = 0


this can be factored as (x-3)(x-2) = 0

so x = 2 or 3

Answer 4

5/x + 3 - 1/x = 1/2
multiply by x =
5 + 3 - 1 = 1/2x
resolve
1/2x = 7
x = 14
Any other answer is simply wrong because there isn't a quadratic equation. Maybe the problem was printed incorrectly?

Answer 5

Multiply both sides by 2x(x+3)
10x-2(x+3)=x(x+3)
10x-2x-6=x^2+3x
8x-6=x^2+3x
x^2-5x+6=0
(x-2)(x-3)=0
x=2 and 3

I hope this helps!

Answer 6

5/(x+3) -1/x = 1/2
first, we need to subtract the fractions 5/(x+3) and 1/x
to do that, we need
the least common multiple for x+3 and x, what is x(x+3)
5/(x+3) -1/x = 1/2
(5x-1(x+3))/(x(x+3))=1/2
(5x-x-3)/(x(x+3))=1/2
(4x-3)/(x(x+3))=1/2
A/B=C/D <==> AD=BC
we have x(x+3)=2(4x-3)
x^2+3x=8x-6
x^2-5x+6=0
the solutions for this quadratic expression are x=2 and x=3
I hope this helps!
good luck

Answer 7

5/(x+3) - 1/x =1/2

multiply both sides by x(x+3)

5x-(x+3)=x(x+3)/2

8x-6=x(x+3)

x^2-5x+6=0

which factors into (x-3)(x-2)

So x=3 and x=2