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If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the

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Bunuel
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If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the [#permalink] New post   20 Nov 2017, 11:26
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If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?


A. −60
B. −12
C. −1
D. 1
E. 2
F. 5

Show: :: OA
A, C, D, and F


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A,C,D,F
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Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the [#permalink] New post   28 Nov 2017, 03:26
Need either a closer look or discerning eye to get solution on the fly :) otherwise its would literally waste much time
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Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the [#permalink] New post   29 Nov 2017, 05:46
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Bunuel wrote:
If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?


A. −60
B. −12
C. −1
D. 1
E. 2
F. 5

Show: :: OA
A, C, D, and F




Here the equation can be written as-

\(\frac{5(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{5(x + 1)}{(x - 2)}\)

or \(\frac{(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{(x + 1)}{(x - 2)}\)

or \(\frac{(x + 12)(x+1)}{(x + 12)(x-2)} = \frac{(x + 1)}{(x - 2)}\)



Now looking at the values we notice only when x=2 & x =-12, the equation is not possible, rest all are the possible values.
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then which of the following are possible values of x? [#permalink] New post   06 Nov 2018, 06:02
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If \(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}\) then which of the following are possible values of x?

Indicate all such values.

A. − 60

B. − 12

C. − 1

D. 1

E. 2

F. 5
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Yiddo_Bhushan
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Re: then which of the following are possible values of x? [#permalink] New post   09 Nov 2018, 11:05
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Quick Approach to these type of Questions Solve for the Denominator = 0 and REJECT those values for 'x' as the Denominator can't be 0.

In this question x not equal to 2 & -12 AS IT WILL MAKE THE Denominator 0.
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Re: then which of the following are possible values of x? [#permalink] New post   11 Nov 2018, 00:40
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Carcass wrote:
If \(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}\) then which of the following are possible values of x?

Indicate all such values.

A. − 60

B. − 12

C. − 1

D. 1

E. 2

F. 5



\(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}.......(5x^2 + 65x + 60)*(x-2)=(x^2 + 10x -24)*(5x+5).........5(x^2+13x+12)*(x-2)=(x^2 + 10x -24)*5(x+1).........(x+12)(x+1)*(x-2)=(x + 12)(x -2)*(x+1)\)
so LHS=RHS therefore all values of x are possible except when the denominator becomes 0....
1) x-2=0 means x=2
2) \(x^2 + 10x -24=0........x^2+12x-2x-24=0....(x+12)(x-2)=0\) so x can be 2 or -12
combined x should not be 2 and -12 and rest of the values are possible.
Thus A, C, D and F
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Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the [#permalink] New post   14 Jun 2019, 08:14
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pranab01 wrote:
Bunuel wrote:
If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?


A. −60
B. −12
C. −1
D. 1
E. 2
F. 5

Show: :: OA
A, C, D, and F




Here the equation can be written as-

\(\frac{5(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{5(x + 1)}{(x - 2)}\)

or \(\frac{(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{(x + 1)}{(x - 2)}\)

or \(\frac{(x + 12)(x+1)}{(x + 12)(x-2)} = \frac{(x + 1)}{(x - 2)}\)

or \(\frac{(x+1)}{(x-2)} = \frac{(x + 1)}{(x - 2)}\).

Now looking at the values we notice only when x=2, the equation is not possible, reset all are the possible values.




also, x=-12 gives undefined value, so this is also not possible
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Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the [#permalink] New post   14 Jun 2019, 22:18
jelal123 wrote:
also, x=-12 gives undefined value, so this is also not possible



Thanks. might be an oversight :shock:
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Re: then which of the following are possible values of x? [#permalink] New post   30 Jul 2021, 09:20
Carcass , can you please explain the answer of the question. Thanks in advance.
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Re: then which of the following are possible values of x? [#permalink] New post   30 Jul 2021, 11:07
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Ahasunhabib999 wrote:
Carcass , can you please explain the answer of the question. Thanks in advance.


Dear Sir the two explanations above (the short and the longest one ) are both perfect.

There is not a real shortcut
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Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the [#permalink] New post   24 Oct 2021, 21:28
Bunuel wrote:
If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?


A. −60
B. −12
C. −1
D. 1
E. 2
F. 5

Show: :: OA
A, C, D, and F


Kudos for correct solution.


This problem makes no sense for me :lol: :lol: :lol: :lol:
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Re: then which of the following are possible values of x? [#permalink] New post   11 Aug 2022, 02:22
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