Solve {x/(x+1)}^2 - 5{x/(x+1)} + 6 = 0

Dr.Dipin Singh   10 years AGO

{x/(x+1)}^2 - 5{x/(x+1)} + 6 = 0
let
x/(x+1)=y;
then
y^2-5y+6=0
y=2,3
Then
x/(x+1)=y =2; x= -2
x/(x+1)=y=3; x=-3/2

Like? Yes (37) | No (5)  

aviral bhargava   10 years AGO

let (x/x+1)=a
we get the equation as a^2-5a+6=0
=> a^2-3a-2a+6=0
=> (a-3)(a-2)=0
On solving the above given equation we get the values of a as
a=3 or 2
Since a= (x/x+1)
Now finding the values of x
Firstly,

x/x+1=2
From above
We get x=-2

Keeping (x/x+1)=3
We get x=-3/2
Hence the answer is -2,-3/2

Like? Yes (12) | No (5)  

kiruthika   10 years AGO

The Quadratic equation is
{x/(x+1)}^2 - 5{x/(x+1)} + 6 = 0

{x/(x+1)}^2 - 2{x/(x+1)} - 3{x/(x+1)} + 6 = 0
Taking {x/(x+1)} outside we get,

{x/(x+1)}[{x/(x+1)}- 2]- 3[{x/(x+1)}-2] = 0

[{x/(x+1)}-3][{x/(x+1)}-2] = 0,then we get

==> [{x/(x+1)}-3] = 0
{x/(x+1)} = 3
x = 3x + 3
-2x = 3
x = -3 /2, similarly the other one

==> [{x/(x+1)}-2] = 0
{x/(x+1)} = 2
x = 2x + 2
-x = 2
x = -2
So the answer for the quadratic equation is
option 9 ==> x =-3/2 and x=-2

Like? Yes (9) | No (2)  

Varunraj Reddy   10 years AGO

Given equation
{x/(x+1)}^2-5{x/(x+1)}+6=0
by simplifying we get
2x^2+7x+6=0
by solving we get values of x=-2,-3/2 option 9)

Like? Yes (8) | No (4)  

Saidinesh   10 years AGO

X^2/(X+1)^2-5(x)/(X+1)+6=0;
x^2-5X(x+1)+6(X+1)^2=0;
x^2-5x^2-5x+6x^2+6+12x=0;
2x^2+7x+6=0;
SOLVING THIS
2X(X+2)+3(X+2)=0;
THEN
X=-2;
X=-3/2;

Like? Yes (9) | No (5)  

Lavankumar Reddy   10 years AGO

{x/(x+1)}^2 - 5{x/(x+1)} + 6 = 0

Let a=x/x+1

a^2-5a+6=0

a^2-3a-2a+6=0

(a-2)(a-3)=0

then subsitute a value

{(x/(x+1))-2}{(x/(x+1)-3}=0

{x-3x-3/(x+1)}{-x-2x-2/x+1}=0

{-2x-3/(x+1)}{-x-2/(x+1)}=0

(-2x-3)(-x-2)/(x+1)^2=0

(-2x-3)(-x-2)=0

-2x-3=0 and -x-2=0

-2x=3 and -x=2

x=-3/2 and x=-2

Like? Yes (6) | No (3)  

Murali Konduru   10 years AGO

take ((x/x+1)) as y i the above equation so the equation becomes y^2-5y+6=0 so by solving the equation we get y=3,2 and equating y=(x/(x+1))
3=x/x+1,2=x/x+1
we get x=-2,x=-3/2 so option 9 is the correct answer

Like? Yes (3) | No (2)  

Grishma Shah   10 years AGO

here take x/x+1=y
thus putting value in equation here y^2-5y+6=0
here solving,we get y=3,y=2
thus x/x+1=3 , x/x+1=2
after solving both equations,we get x=-3/2 and x=-2
so option 9 is correct.

Like? Yes (6) | No (5)  

Devendra Marghade   10 years AGO

{x/(x+1)}^2 - 5{x/(x+1)} + 6 = 0
2x^2+7x+6=0
(x+2)(2x+3)=0
x=-2, -3/2

Like? Yes (4) | No (3)  

ASHISH KUMAR MISHRA   10 years AGO

let Y= x/(x+1); now y^2-5y+6=0;
Now y=2,3
x/(x+1)=2 => x=-2 and x/(x+1)=3 => x=-3/2;
so ans is -2,-3/2

Like? Yes (3) | No (2)  

Anantharaman   10 years AGO

lets assume y= (x/x+1)

so eqn => y^2-5y+6=0

Solving we will get y=3,2

Now substituting (x/x+1)=y

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

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

So solution of x : -2, -3/2
Option 9

Like? Yes (4) | No (3)  

sravani   10 years AGO

x/x+1=y
y^2-5y-6=0
y=2,3
and substitute these values and we get -2,-3/2

Like? Yes (3) | No (2)  

Mahalakshmi   10 years AGO

{(x/(x+1))-3}{(x/(x+1))-2}=0 equation we will get
solving this get x=-2,-3/2

Like? Yes (1) | No (1)  

Vaishali Dhiman   10 years AGO

ans is option 9
{x/(x+1)}^2 - 5{x/(x+1)} + 6 = 0

taking LCM
{x^2-5(x+1)+6(x+1)^2}/(x+1)^2=0
{x^2-5(x+1)+6(x+1)^2}=0
2x^2+7x+6=0
2x^2+3x+4x+6+0
x(2x+3)+2(2x+3)=0
(x+2)(2x+3)=0
x=-2, -3/2

Like? Yes (1) | No (1)  

Srinath   10 years AGO

SOLVE X^2-5X(X+1)+6(X^2+2X+1)=0
2X^2+7X+6=0
X=-7+(49-48)/4
THEN WE GET X=-1.5, -2

Like? Yes (3) | No (3)  

dhyanendra mani tripathi   10 years AGO

let (x/x+1)=y
we get y^2-5y+6=0
solving we get y= 2,3
=> (x/x+1)=y= 2 and 3
hence we get
x/x+1=2 => x= -2
x/x+1=3 => x= -3/2

Like? Yes (2) | No (2)  

ravinder reddy   10 years AGO

take x/(x+1)=y
then it becomes
y^2-5y+6=0
by factorization
y=2,3
now take y=2
substitute y value
x/(x+1)=2
x=-1 , similarly with y=3 then x=-3/2

Like? Yes (2) | No (2)  

DHAKAD NEETENDRA SINGH   10 years AGO

let x/(x+1)=t

t^2-5t+6=0
(t-3)(t-2)=0
t=3,2

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

Like? Yes (2) | No (2)  

Suman   10 years AGO

2x^2+7x+6=0
so x=-2,-3/2

Like? Yes (2) | No (3)  

viveka   10 years AGO

let y be x/x+1
y2-5y+6=0

y=3
x/x+1=3
x=-3/2

y=2
x/x+1=2
x=-2

Like? Yes (1) | No (2)  

sivaraman   10 years AGO

x/x+1=3
or
x/x+1=2 x=2x+2
x=3x+3 x=-2
x=-3/2

Like? Yes (1) | No (2)  

Sajal Garg   10 years AGO

9) -2, -3\2
a) (-2/-1)^2-5(-2/-1)+6=4-10+6=0
b) [(-3/2)/{(-3/2)+1)}]^2 -5[(-3/2)/{(-3/2)+1)}]+6 = {(-3/2)/(-1/2))}^2-5{(-3/2)/(-1/2))}+6=3^2-5(3)+6=9-15+6=0

Like? Yes (1) | No (3)