Please help me with this equation?

Question

24 / x-3 = 72 / x + 3
please explain as you solve and check!
Your help is very much appreciated!!

Answer 1

Solve as a proportional Problem

24/x - 3 = 72 / x + 3

The means 72(x - 3)

The extremes 24(x - 3)

24(x + 3 = 72(x - 3)

24x + 72 = 72x - 216

Transpose 24x

24x + 72 - 24x = 72x - 216 - 24x

72 = 48x - 216

Transpose 216

72 + 216 = 48x - 216 + 216

288 = 48x

Divide both sides of the equation by 48

288 / 48 = 48x / 48

288 / 48 = x

6 = x

- - - - - - - -s-

Answer 2

Multiply both sides by (x - 3) (x + 3)
24 (x + 3) = 72 (x - 3)
24 x + 72 = 72 x - 216
216 + 72 = 72 x - 24 x
288 = 48 x
x = 288 / 48
x = 6

Answer 3

24 / (x-3) = 72 / ( x + 3)

you don't want your x as a denominator. so let's start by multiplying it out of there. don't forget: whatever you do to one side, you have to do to the other.

24(x-3) / (x-3) = 72 (x-3) / (x+3)
24 = 72(x-3) / (x+3)
24(x+3) = 72(x-3)(x+3)/(x+3)
24(x+3) = 72(x-3)

multiply the factors out:

24x+72 = 72x-216

you want your x to one side, and numbers to the other:

24x + 72 - 72 = 72x -216 - 72
24x = 72x - 288
24x-72x = 72x - 288 -72x
-48x = -288

divide by -48 on both sides to solve for x:

x = 6

and to verify, everytime you see an x in the original equation, replace it with its now-known value of 6:

24 / x-3 = 72 / x + 3
24 / (6-3) = 72 / (6+3)
24/3 = 72/9
8 = 8

*tada*

good luck!

Answer 4

24 / x-3 = 72 / x + 3
= 72(x-3) = 24(x+3)
= 72x-216 = 24x+72
= 72x-24x = 72+216
= 48x = 288
= x = 288/48
= x = 6

answer is 6.

Answer 5

24/(x - 3) = 72/ (x +3)
multiply both sides by (x-3)(x+3)
giving 24(x+3) = 72(x-3)
expand the expressions
24x + 72 = 72x - 216
subtract 24x from both sides
72 = 48x - 216
add 216 to both sides
48x = 288
divide both sides by 48
x = 6

Answer 6

I assume it is 24/(x-3)=72/(x+3)

minus 72/(x+3) from both sides:

24/(x-3) - 72/(x+3) = 0

make both the denominators (x+3)(x-3) by multiplying the first 'part' by (x+3) and the second by (x-3) to get

24(x+3)/(x+3)(x-3) - 72(x-3)/(x+3)(x-3) =0

which simplifies to:

(24(x+3)-72(x-3))/(x+3)(x-3)=0

which simplified to:

(288-48x)/(x+3)(x-3) = 0

therefore 288-48x=0
48x=288
x=6

Answer 7

24/(x-3) = 72/(x+3)
24/(x-3) - 72/(x+3)= 0
{24(x+3) -72(x-3)} / [x^2 - 9] = 0
{24x+72} - {72x-216} /{x^2 -9} = 0
[24x + 72 - 72x +216] / [x^2 - 9] = 0
[ -48x + 288] / [x^2 - 9] = 0
The numerator should be zero
48x = 288
x = 288 / 48 = 6....Ans.
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Answer 8

Mutiply both sides by (x-3) gives 24 = 72(x-3)/x+3)
Multiply both sides by (x+3) gives 24 (x+3) = 72(x-3)
Simplify by dividing 72 by 24 (=3) gives (x+3) = 3(x-3)
so x+3 = 3x -9 .
So x = 3x -9 -3 = 3x -12.
So 2x = 12
So x = 6

Answer 9

24/(x - 3) = 72/(x + 3), x cannot be 3 or -3
72(x - 3) = 24(x + 3)
72x - 216 = 24x + 72
48x = 288
x = 6

Answer 10

24/x=72/x +6; 48/x=-6; x=-8

if x-3 and x+3 is in paranthesis, 24(x+3) = 72(x-3); 2x=12; x=6