Help please with this equation 2 / (x+1)=2x / (2x-3)+3?

Question

I do not have a clue where to begin on solving this and any help that you could give me would be great.
Thanks

Answer 1

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

Answer 2

Why all the complexity ?

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

The denominator on the right hand side simplifies to 2x-3+3, which = 2x. The bracket doesn't do anything when the following operator is + or -.

Therefore:

2/(x+1) = 2x/2x =1

Therefore 2/(x+1) = 1

(can be written as 2/(x+1) = 1/1

Cross multiplying gives

2 =x+1

Therefore x =1

Answer 3

tricky first

we have

2x
------- + 3
2x-3

the common factor is 2x-3

which means

2x+3(2x-3)
---------------
2x-3

(((important note this is not
(2x+3)(2x-3)
-----------------
2x-3 )))

this is

2x+6x-9
------------
2x-3


the left side

2
---
x+1

now multiply
both sides by 2x-3

4x-6
------ =2x+6x-9
x+1

which is

4x-6
------ =8x-9
x+1

now multiply both sides by x+1

gives 4x-6=(8x-9)*(x+1)

right side

8x^2-x-9

now move left into right
0=8x^2-5x-3

which has the solution
(8x+3)(x-1)=0=8x^2-5x-3
therefore
either (8x+3) or (x-1) is equal to zero
if 8x+3
then x has to be minus and 3/8=-0.375
or
if (x-1) is the case then x=1

u asking how u turn
8x^2-5x-3
into (8x+3)(x-1)
the answer practice, blood sweat and tears that is what homework is for

a few hints think what times what makes plus 8
and what times what makes minus 3
then play jigsaws with the minus 5

Be careful all other answers are wrong

(((uday k

went wrong at the end for 1*-1=1 not -3)))

Answer 4

multiply both sides by (x+1)(2x)
4x=2x^2+2
2x^2-4x+2=0
(2x-1)(x-2)
use the 1st one
2x-1=0
2x=1
x=1/2
use the 3nd one
x-2=0
x=2
so the roots of x= 1/2,2

Answer 5

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

2= 2xsq +2x/2x (3s cancel out)

2 = x + 1

x=1

Substitute 1 back into your original equation and you will discover that this answer is correct.

Answer 6

69

Answer 7

Clue: multiply both sides by the denominator

now do your own homework

Answer 8

2/(x+1)=2x/(2x-3)+3
=2x+3(2x-3)/(2x-3) (Take L.C.M )
=(8x-9)/(2x-3)
2(2x-3)=(8x-9)(x+1) (Cross Multiply)
4x-6=8x^2-x-9
8x ^2-5x-3=0
8x ^2-8x+3x-3=0
(8x+1)(x-1)=0
so x values are -1/8 and 1

Answer 9

2(x+1) = 2x(3x-3)+3
2x+2 = 4xx-6x+3
2x+2 = 4xx - 6x +3
2x-6x = 4xx +3-2
-4x = 4xx+1
divide both sides by -4x
-4xx /4x= 4x +1/-4x
x = -1+1
x = 0

Answer 10

Uday k almost right, but there is one wrong answer. x2=-3/8 (not -1/8), x1=1. It is true.

Other answers are wrong.