Solve. 5/x+1 = x+2/x+1?

...5........x+2
---------=---------
x+1......x+1

5(x+1)=(x+2)(x+1)
5x+5=x^2+3x+2
x^2+3x-5x+2-5=0
x^2-2x-3=0
(x-3)(x+1)=0
x-3=0 x+1=0
x=3 x=-1

so the answer is c. 3

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

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
x+(2)/(x)+1=(5)/(x)+1

Find the LCD (least common denominator) of x+(2)/(x)+1+(5)/(x)+1.
Least common denominator: x

Multiply each term in the equation by x in order to remove all the denominators from the equation.
x*x+(2)/(x)*x+1*x=(5)/(x)*x+1*x

Simplify the left-hand side of the equation by canceling the common factors.
x^(2)+x+2=(5)/(x)*x+1*x

Simplify the right-hand side of the equation by simplifying each term.
x^(2)+x+2=x+5

Since x contains the variable to solve for, move it to the left-hand side of the equation by subtracting x from both sides.
x^(2)+x+2-x=5

Since x and -x are like terms, add -x to x to get 0.
x^(2)+2=5

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x^(2)=-2+5

Add 5 to -2 to get 3.
x^(2)=3

Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.
x=\~(3)

First, substitute in the + portion of the \ to find the first solution.
x=~(3)

Next, substitute in the - portion of the \ to find the second solution.
x=-~(3)

The complete solution is the result of both the + and - portions of the solution.
x=square root of (3),-square root of (3)_x = 1.73,-1.73

c. 3

divide out (x+1) from both sides to get 5=x+2
so x=3

d most ez way 2 answr ths is 2 substitute each value in2 d EQ (trial & error method) =P
for d workin: (im assumin ur Q is like ths)

5/(x+1) = (x+2) / (x+1)
5(x+1) = (x+2)(x+1) <!----- cross multiply
5x +5 = x^2 +x +2x +2
x^2 -2x -3 = 0

use d formula [-b^2 ± √(b^2 - 4ac)] / 2a

x= [-(-2)^2 ± √([-2]^2 - 4[1][-3])] / 2[1]
x= 3, -1

from d options, d answr shud b C (3)
hope ths helps =)

x=3

/=i think divide
5(x+1) / (x+1) = x + 2, (x+1) / (x+1) = 1
hence, 5(1) = x + 2
x = 5 - 2
x = 3
so, the answer is C

5/(x + 1) = (x + 2)/(x + 1)
5 = x + 2
x = 5 - 2
x = 3
(answer c)

Multiply x+1 on both sides so you get 5=x+2
subtract 2 from both sides so 3=x or c.

Presentation is such that equation MUST be read as :-

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

5 + x = x ² + 2 + x

3 = x ²

x = ± √3

However it may be that you mean , NOT AS GIVEN , but :-

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

5 = x + 2

x = 3

OPTION c

PS
It is important to present questions in a clear and unambiguous fashion.

There is a solution but it's not listed here.

x = positive and negative sq. root of 3

if you plug and chug 3 into x it doesn't make sense. 5/3 + 1 = 8/3 and 3 + 2/3 + 1 = 14/3. 8/3 does not equal 14/3

c. 3
God bless you.