Solve the problem?

Question

((4)/(x)) + ((3)/(x-3)) = ((x)/(x-3)) - ((1)/(3))

Answer 1

4/x + 3/(x-3) = x/(x-3) - 1/3
3(4(x-3) + 3x)/(3x(x-3)) = (3x^2 - x(x-3))/(3x(x-3))

Cancel the common denominator
Note: x = 0 and x = 3 are factors of the denominator and are not permissible solutions.

3(4(x-3) + 3x) = (3x^2 - x(x-3))
3(4x-12+3x) = 3x^2 - x^2 + 3x
21x - 36 = 2x^2 + 3x
2x^2 - 18x + 36 = 0
x^2 - 9x + 18 = 0
x^2 - 6x - 3x + 18 = 0
x(x-6)-3(x-6)=0
(x-6)(x-3) = 0
x = 6
x= 3

x=3 is not allowed

The only solution is x=6

Answer 2

(4 / x) + 3 / (x - 3) = x / (x - 3) - 1 / 3
X both sides by 3 x (x - 3)
12 (x - 3) + 9 x = 3 x² - (x) (x - 3)
12x - 36 + 9x = 3 x² - x² + 3x
21x - 36 = 2x² + 3x
2x² - 18x + 36 = 0
x² - 9x + 18 = 0
(x - 6) (x - 3) = 0
x = 3 , x = 6

Answer 3

Multiply through by 3x(x-3).

4*3*(x-3) + 3*3x = x*3x - x(x-3)
12x - 36 + 9x = 3x^2 - x^2 + 3x
21x - 36 = 2x^2 + 3x
2x^2 - 18x + 36 = 0
x^2 - 9x + 18 = 0
(x - 3)(x - 6) = 0
x = 3 or x = 6
But x = 3 is not allowed, it causes division by zero.

Answer: x = 6.

Answer 4

((4)/(x)) + ((3)/(x-3)) = ((x)/(x-3)) - ((1)/(3))

To make the denominator same of both sides of the equation, multiply both sides of the equation by 3x(x-3)
12(x-3) + 9x = 3x^2 - x(x-3)
12x -36 +9x = 3x^2 -x^2 +3x

Arranging the equation decreasing order of power, to give,
2x^2 - 18x +36 =0
x^2 -9x +18 =0
(x-3) (x-6) =0
x=3 OR x=6 .............ANS

hope this helps!! :-)

Answer 5

Multiply both sides by 3x(x-3),
12(x-3) + 9x = 3x^2 - x(x-3)
2x^2-18x+36 = 0
x^2-9x+18 = 0
(x-3)(x-6) = 0
x = 3, 6

Answer 6

((4)/(x)) + ((3)/(x-3)) = ((x)/(x-3)) - ((1)/(3))
Multiply both sides of the equation by 3x(x-3)
12(x-3) + 9x = 3x^2 - x(x-3)
12x -36 +9x = 3x^2 -x^2 +3x
2x^2 - 18x +36 =0
x^2 -9x +18 =0
(x-3)(x-6) =0
x=3 or x=6

Yep, I should have added x<>3 so only x=6 allowed.
Bad error!!

Answer 7

Multiply both sides by 3x(x-3) to get:

12(x-3) + 9x= 3x**2-x(x-3)

12x-36+9x=3x**2-x**2+3x
0=2x**2-18x+36
0=(2x-6)(x-6)
x=6
x=3

but at x= 3 the original equation is undefined, so the solution is that x=6

Answer 8

x = 3 or x = 6

You need to multiply all 4 parts of the equation by 3(x)(x-3)
so ((4)(3)(x)(x-3))/(x) + ((3)(3)(x)(x-3))/(x-3) = ((x)(3)(x)(x-3))/(x-3) - ((1)(3)(x)(x-3))/(3)

This will give you
12(x-3) + 9x = 3x(squared)-1x(squared) +3x

Then multiply out 12(x-3) and add the x(squared)s

12x -36 + 9x = 2x(squared) + 3x

Simplify to 2 (x(squared) -9x +18) = 0

Solve for x using 2(x-6)(x-3) = 0

so x = 6 or x =3

Answer 9

4/x + 4/x-3 = (x/x-3) - 1/3
(3/x-3) - (x/x-3) = -4/x - (1/3)
3-x/x-3 = (-12 + -x)/3x
(3-x) * 3x = (x-3) * (-12 + -x)
9x - 3x^2 = -12x - x^2 + 36 - 3x
9x + 12x + 3x = 3x^2 - x^2 + 36
24x = 2x^2 + 36
2x^2 + 24x + 36 = 0

Assume 2x = y

y + 24x + 36 = 0

Due to the binomial theorem this equals to:

(y+6)

Since y = 2x

(2x+6)^2

Good luck.