x-1/x-2+x-3/x-4=10/3?

Answer 1

x-1/x-2+x-3/x-4=10/3

x - 1/x - 2 + x - 3/x - 4 = 10/3

multiply both sides by 3x,

3x² - 3 - 6x + 3x² - 9 - 12x = 10x
let 6x² - 28x - 12 = 0
2(3x² - 14x - 6) = 0

let a = 3, b = -14, c = -6

use the formula = [ -b +/- square root (b² - 4ac) ] / 2a

= [ -(-14) +/- square root (-14² - 4(3)(-6) ] / 2(3)
= [ 14 +/- square root (196+72) ] / 6
= 14 +/- √268/6
= 14/6 +/- √268/6
= 7/3 +/- √268/6

Answer 2

X=5

Answer 3

3^ (x+2) + 2 = 12 - 3^(x+4) or 3^(x+2) + 3^(x+4) = 10 or 3^(x+2) + 3^(x+2) 3^2 = 10 or 3^(x+2)[ a million + 3^2] = 10 or 3^(x+2)* 10 = 10 or 3^( x+2) =a million or 3^(x+2) = 3^0 [ IF A^n = A^ m THEN n = m ] so x+2 = 0 or x= - 2 answer

Answer 4

I think you meant

(x - 1) / (x - 2) + (x - 3) / (x - 4) = 10/3 and we need to solve it for x.

3[(x - 1) ( x - 4) + (x - 3) (x - 2)] = 10 (x - 2) (x - 4)

3[ x^2 - 5x + 4 + x^2 - 5x + 6] = 10 (x^2 - 6x +8)

3(2x^2 - 10x + 10) = 10x^2 - 60x + 80

6x^2 - 30x + 30 = 10x^2 - 60x + 80

Subtracting the LHS from the RHS

4x^2 - 30x + 50 = 0

2x^2 - 15x + 25 = 0

(2x - 5) (x - 5) = 0

So 2x - 5 = 0 and x -5 = 0

x = 5/2 and 5

Answer 5

x=5

Answer 6

x-1/x-2 + x-3/x-4 = 10/3
Multiply both sides by the LCM which is
3(x-2)(x-4)

3(x-2)(x-4)((x-1/x-2 + x-3/x-4 = 10/3)

3(x-4)(x-1) + 3(x-2)(x-3) = 10(x-2)(x-4)
(3x-12)(x-1) + (3x-6)(x-3) = (10x -20)(x-4)
3x^2 -3x -12x + 12 + 3x^2 - 9x -6x + 18 = 10x^2 -40x -20x + 80
6x^2 -30x + 30 = 10x^2 - 60x + 80
6x^2 -30x + 30 - 10x^2 + 60x -80 = 10x^2 -60x + 80 -10x^2 + 60x -80
-4x^2 +30x -50 = 0
Multiply the equation by -1
(-1)(-4x^2 + 30x - 50 = 0)
4x^2 -30x + 50 = 0
Factor
(4x - 10) (x - 5) = 0
To make this equation true,
4x - 10 = 0 or x - 5 = 0
If 4x - 10 = 0
4x = 10
x = 10/4
x = 5/2
If x - 5 = 0
x = 5

Answer 7

add (x-1)=t
=>t/(t-1) + (t-2)/(t-3)=10/3
=>t(t-3) + (t-2)(t-1)=10/3(t-1)(t-3)
=> now it's easy to solve

Answer 8

x + x -x/2 - 3/4x = 10/3+6
-x/4 = 28/3
x = - 114 / 3

Answer 9

After combining like terms and reducing you get:
x - 2/x =14x/3

multiplying all by x will convert this to a quadratic equation:

x^2 - 4.67x -2 =0

using the quadratic equation you get (approximately):

x=5.07 AND x=-0.39

Answer 10

use parathesis next time....it's too confusing, the equation could be set up so many ways. if it's x-1 use (x-1).