If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?

Question

If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x? 
 A. √2 
 B. ±√2 
 C. 1 
 D. 2 
 E. √5

*An answer will be posted in 2 days.

chetan2u · Answer

Hi,

two ways to do it..

1) substitute value
when you substitute value of x as √2 , we get the required answer, BUT the value √2 is also in B..
check for -√2 , you will get answer as B..

2) proper method
 \frac{1}{x(x+1)}+\frac{1}{(x+1)(x+2)}=\frac{1}{(x+1)} ....
 \frac{1}{(x+1)}(\frac{1}{x}+\frac{1}{(x+2)}-1)=0 ....
so either \frac{1}{(x+1)}=0, that is not posible as numerator cannot be 0..
so  (\frac{1}{x}+\frac{1}{(x+2)}-1)=0......\frac{x+2+x-x^2-2x}{x(x+2)}=0 ....
 x+2+x-x^2-2x=0........x^2=2.... or x= ±√2 
B

MathRevolution · Answer

If we solve the question, we get x=±√2.

Senthil1981 · Answer

This is a straight algebraic equation with no catch. How come listed as 600-700 category question ?

Arsh4MBA · Answer

From the Question stem cancel out the common denominator x+1;

so it becomes (1/x)+(1/x+2)=1;

Solving this we get x+2+x = x(x+2);

2x+2=x^+2x
so x= ±√2 
 Ans:B

KanishkM · Answer

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

Take the LCM in LHS, making the LHS as

\frac{2x+2}{x*(x+1)* (x+2)}  =  \frac{1}{x+1}

Now if you cross multiply the denominator of LHS to RHS

Equation will be reduced to

2x + 2 = x^2 + 2x

x^2  = 2

Giving answer as  B

mba20202022 · Answer

does the Gmat presents fractions in this way?
the majority of the time in this Qs I only had to make sure I wrote the equation right....

Muthusivakathir · Answer

I don't think GMAT would expect us to waste time in checking the question.
It'll be straightforward most of the time. Not to worry much about that.

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If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?

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If 1/(x(x+1))+1/((x+1)(x+2))=1/(x+1), what is the value of x?

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