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

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Sajjad1994
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If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the [#permalink] New post   Updated on: 27 Nov 2020, 00:15
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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) \(rs^2+r^2\)
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A

Originally posted by Sajjad1994 on 24 Nov 2020, 01:54.
Last edited by Bunuel on 27 Nov 2020, 00:15, edited 1 time in total.
Edited the OA.
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Re: If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the [#permalink] New post   24 Nov 2020, 06:53
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Sajjad1994 wrote:
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) \(rs^2+r^2\)


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

Answer: A
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Re: If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the [#permalink] New post   24 Nov 2020, 11:16
Sajjad1994 wrote:
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) \(rs^2+r^2\)

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

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

Or, \(\frac{(r+s)}{(r-s)}\), Answer must be (A)
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If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the [#permalink] New post   28 Nov 2020, 04:43
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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 = \(\frac{(r + s) (r + s)}{(r + s) (r – s)} = \frac{(r + s)}{(r – s)}\)
[here, we can cancel (r + s) as we already know |r| is not equal to |s|]

Thus, option A is the correct answer.

Correct Answer: Option A
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If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the [#permalink] New post   28 Nov 2020, 09:20
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 \(r \neq s\) since \(|r| \neq |s|\)

IMO A
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If |r| ≠ |s|, then (r^2+2rs+r^2)/r^2-s^2 is equivalent to which of the [#permalink]
28 Nov 2020, 09:20
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