Need help with solving these equations!?

...x.......2
.----- = -----
...3.......x

x^2=6
x=+/-sqrt(6) answer


4x^2+8x-5=0
(2x+5)(2x-1)=0
2x+5=0 2x-1=0
2x=-5 2x=1
x=-5/2 x=1/2 answer

x^2-4x-3=0
a=1 b=-4 c=-3
x=-b+/-sqrt(b^2-4ac)/2a
x=-(-4)+/-sqrt[(-4)^2-4(1)(-3)]/2(1)
x=4+/-sqrt[16+12]/2
x=4+/-sqrt[28]/2
x=4+/-sqrt[4*7]/2
x=4+/-2sqrt(7)/2

.....4+2sqrt(7).......4-2sqrt(7)
x=------------------ , -----------------
.........2.......................2

x=2+sqrt(7), 2-sqrt(7) answer//


....2.............2x
----------- = ------ + 3
..x+1..........2x-3

[ 2/x+1] = 2x/2x-3 +3] (x+1)(2x-3)

2(2x-3)=2x(x+1)+3(x+1)(2x-3)
4x-6=2x^2+2x+3(2x^2-x-3)
4x-6=2x^2+2x+6x^2-3x-9
4x-6=8x^2-x-9
8x^2-x-4x-9+6=0
8x^2-5x-3=0
(x-1)(8x+3)=0
x-1=0 8x+3=0
x=1 8x=-3
x=-3/8 answer

1)
x/3 = 2/x
3x(x/3) = 3x(2/x)
x^2 = 6
x = ±√6

= = = = = = = =

2)
4x^2 + 8x - 5 = 0
4x^2 + 10x - 2x - 5 = 0
(4x^2 + 10x) - (2x + 5) = 0
2x(2x + 5) - 1(2x + 5) = 0
(2x + 5)(2x - 1) = 0

2x + 5 = 0
2x = -5
x = -5/2 (-2.5)

2x - 1 = 0
2x = 1
x = 1/2 (0.5)

∴ x = -5/2 (-2.5) , 1/2 (0.5)

= = = = = = = =

3)
x^2 - 4x - 3 = 0
x^2 - 4x = 3
x^2 - 2x - 2x = 3
x^2 - 2x - 2x + 4 = 3 + 4
(x^2 - 2x) - (2x - 4) = 7
x(x - 2) - 2(x - 2) = 7
(x - 2)(x - 2) = 7
(x - 2)^2 = 7
x - 2 = ±√7
x = 2 ±√7

= = = = = = = =

4)
2/(x + 1) = 2x/(2x - 3) + 3
[x + 1][2x - 3][2/(x + 1)] = [x + 1][2x - 3][2x/(2x - 3) + 3]
2(2x - 3) = 2x(x + 1) + 3(x + 1)(2x - 3)
4x - 6 = 2x^2 + 2x + 3(2x^2 - x - 3)
4x - 6 = 2x^2 + 2x + 6x^2 - 3x - 9
2x^2 + 6x^2 - x - 4x + 6 - 9 = 0
8x^2 - 5x - 3 = 0
8x^2 + 3x - 8x - 3 = 0
(8x^2 + 3x) - (8x + 3) = 0
x(8x + 3) - 1(8x + 3) = 0
(8x + 3)(x - 1) = 0

8x + 3 = 0
8x = -3
x = -3/8 (-0.375)

x - 1 = 0
x = 1

∴ x = -3/8 (-0.375) , 1

Hi,

x/3 = 2/x

x . . 2
-- = ---
3 . . x

x² = 6
. . . . . _
x = ±√6 <==ANSWER



4x² + 8x - 5 = 0

(2x + 5)(2x - 1) = 0

x = -5/2 or x = 1/2 <==ANSWER




x² - 4x - 3 = 0
. . . . . .___________
-(-4) ± √(-4)² - 4(1)(-3)
------------------------------- = x
. . . . 2(1)

. . . .______
4 ± √16 + 12
------------------- = x
. . . . 2


. . . .__
4 ± √28
------------ = x
. . 2

. . . ._
2 ± √7 = x <==ANSWER



2over x+1 = 2x over 2x-3 +3

. 2. . . . .2x
------ = --------- + 3
x+1 . . 2x - 3

Multiply by (x + 1)(2x - 3) to eliminate the fractions.

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

4x - 6 = 2x² + 2x + 6x² - 3x - 9

4x - 6 = 8x² - x - 9

0 = 8x² - 5x - 3

0 = (x - 1)(8x + 3)

x = 1 or x = -3/8 <==ANSWER

I hope that helps!! :-)