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If xy is not equal to 0, then which of the following is the equivalent

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If xy is not equal to 0, then which of the following is the equivalent  [#permalink]

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New post 05 Sep 2017, 00:46
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:06) correct 31% (02:17) wrong based on 134 sessions

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Re: If xy is not equal to 0, then which of the following is the equivalent  [#permalink]

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New post 05 Sep 2017, 01:46
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of \(\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}\)?

A. \(x^6y^2(x + 1)\)

B. \(x^4y^4(x + 1)\)

C. \(2x^4y^4\)

D. \(2x^5y^3\)

E. \(2x^6y^2\)


X^5y^3 + x^5y^3 / (y/x)

= x^5y^2(x+1) *x/y
= x^6y^2(x+1)

A should be correct.


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Re: If xy is not equal to 0, then which of the following is the equivalent  [#permalink]

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New post 05 Sep 2017, 08:05
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of \(\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}\)?

A. \(x^6y^2(x + 1)\)

B. \(x^4y^4(x + 1)\)

C. \(2x^4y^4\)

D. \(2x^5y^3\)

E. \(2x^6y^2\)

\(\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}\)

\(\frac{x^6y^3+x^5y^3}{(\frac{y}{x})}\)

\(\frac{x^5y^3(x +1)}{(\frac{y}{x})}\)

\((x*y^{-1})x^5y^3(x +1)\)

\(x^6y^2(x +1)\)

Answer (A)...
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If xy is not equal to 0, then which of the following is the equivalent  [#permalink]

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New post 06 Sep 2017, 13:42
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of \(\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}\)?

A. \(x^6y^2(x + 1)\)

B. \(x^4y^4(x + 1)\)

C. \(2x^4y^4\)

D. \(2x^5y^3\)

E. \(2x^6y^2\)

It took me a long time to figure out that the denominator is \((\frac{x}{y})^{-1}\), not \((\frac{x}{y}) -
1\)

\(\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}\) =

\(\frac{x^6y^3+x^5y^3}{(\frac{y}{x})}\) =

\((\frac{x}{y}) * (x^5y^3)(x + 1)\) =

\((x^1y^{-1}) * (x^5y^3)(x + 1)\)=

\(x^{(1+5)}y^{(-1+3)} * (x + 1)\)

\(x^6y^2(x + 1)\)

Answer A
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Re: If xy is not equal to 0, then which of the following is the equivalent  [#permalink]

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New post 07 Sep 2017, 16:41
Bunuel wrote:
If xy is not equal to 0, then which of the following, is the equivalent of \(\frac{(x^2y)^3+x^5y^3}{(\frac{x}{y})^{-1}}\)?

A. \(x^6y^2(x + 1)\)

B. \(x^4y^4(x + 1)\)

C. \(2x^4y^4\)

D. \(2x^5y^3\)

E. \(2x^6y^2\)


Let’s first simplify the numerator of the given expression:

(x^6)(y^3) + (x^5)(y^3)

(x^5)(y^3)(x + 1)

Simplifying the denominator, we have: (x/y)^-1 = y/x

Now we have:

(x^5)(y^3)(x + 1)/(y/x) = (x^5)(y^3)(x + 1)*(x/y) = (x^6)(y^2)(x + 1)

Answer: A
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Re: If xy is not equal to 0, then which of the following is the equivalent   [#permalink] 07 Sep 2017, 16:41
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