If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the

Question

If |r| ≠ |s|, then  \frac{r^2+2rs+s^2}{r^2-s^2}  is equivalent to which of the following?

(A)  \frac{r+s}{r-s}

(B)  rs^2

(C)  2rs

(D)  \frac{r-s}{r+s}

(E)  rs^2+r^2

BrentGMATPrepNow · Answer

\frac{r^2+2rs+s^2}{r^2-s^2}=\frac{(r+s)(r+s)}{(r+s)(r-s)}=\frac{(r+s)}{(r-s)}

Answer: A

Abhishek009 · Answer

\frac{r^2+2rs+s^2}{r^2-s^2}

Or,  \frac{(r+s)^2}{(r+s)(r-s)}

Or,  \frac{(r+s)}{(r-s)} , Answer must be (A)

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • The values of |r| and |s| are not equal

To find  
We need to determine
 • The value of the given expression  \frac{r^2+2rs+s^2}{r^2-s^2}

Approach and Working out  
Simplifying the numerator and the denominator individually,
 •  r^2 + 2rs + s^2 = (r + s)^2 = (r + s) (r + s) 
•  r^2 – s^2 = (r + s) (r – s)

Hence, the value =  \frac{(r + s) (r + s)}{(r + s) (r – s)} = \frac{(r + s)}{(r – s)}

Thus, option A is the correct answer.

Correct Answer: Option A

Kinshook · Answer

Asked: If |r| ≠ |s|, then  \frac{r^2+2rs+s^2}{r^2-s^2}  is equivalent to which of the following?

r^2+2rs+s^2 = (r+s)^2 
 r^2 - s^2 = (r+s)(r-s)

\frac{r^2+2rs+s^2}{r^2-s^2}= \frac{(r+s)^2}{(r+s)(r-s)}= \frac{r+s}{r-s} 
It is given that  r 
eq s  since  |r| 
eq |s|

IMO A

If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards