SOLUTION: please help me on this and explain it! I'm really stuck on iy and i dont know how to do it. (2x/(x+3))-5=1/(x+3)

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Question 428302: please help me on this and explain it!
I'm really stuck on iy and i dont know how to do it.
(2x/(x+3))-5=1/(x+3)
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
(2x/(x+3))-5=1/(x+3)
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Multiply thru by (x-3) to get:
2x -5(x-3) = 1
---
2x-5x+15 = 1
-3x = -14
x = 14/3
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Cheers,
Stan H.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your formula is:

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

add 5 to both sides of the equation and subtract (1/(x+3)) from both sides of the equation to get:

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

since the denominators are the same, you can add the 2 fractions together on the left side of the equation to get:

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

multiply both sides of the equation by (x+3) to get:

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

simplify to get:

2x - 1 = 5x + 15

subtract 5x from both sides of the equation and add 1 to both sides of the equation to get:

2x - 3x = 15 + 1

combine like terms to get:

-3x = 16

divide both sides of the equation by -3 to get:

x = - (16/3)

that should be your answer.

replace x with - (16/3) in your original equation and solve to see if the original equation is true.

your original equation is:

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

replace x with - (16/3) to get:

((2 * (-16/3)) / ((-16/3) + 3)) - 5 = (1 / ((-16/3) + 3))

*** note that (-16/3) + 3 = (-16/3) + 9/3 = (-16 + 9)/3 = (-7/3).

simplify to get:

((-32/3) / (-7/3)) - 5 = (1/(-7/3))

simplify further to get:

(-32/3) * (-3/7) - 5 = (-3/7)

simplify further to get:

(32/7) - 5 = (-3/7)

simplify further to get:

(32/7) - (35/7) = (-3/7)

simplify further to get:

(-3/7) = (-3/7) which is true, confirming the value of x is good.

the value of x is equal to (-16/3)