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If a and b are constants such that are constants such that ax/(x^2 - 1

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 763
If a and b are constants such that are constants such that ax/(x^2 - 1  [#permalink]

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04 Feb 2019, 10:47
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

33% (03:06) correct 67% (02:41) wrong based on 9 sessions

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GMATH practice question (Quant Class 13)

If $$a$$ and $$b$$ are constants such that $$\,\,{{ax} \over {{x^2} - 1}} + {b \over {x - 1}} = {{2x - 1} \over {{x^2} - 1}}\,\,$$ for every $$x > 1$$, what is the value of $$a - b$$ ?

(A) -2
(B) -1
(C) 0
(D) 2
(E) 4

Source: https://www.gmath.net

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

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Re: If a and b are constants such that are constants such that ax/(x^2 - 1  [#permalink]

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04 Feb 2019, 11:02
fskilnik wrote:
GMATH practice question (Quant Class 13)

If $$a$$ and $$b$$ are constants such that $$\,\,{{ax} \over {{x^2} - 1}} + {b \over {x - 1}} = {{2x - 1} \over {{x^2} - 1}}\,\,$$ for every $$x > 1$$, what is the value of $$a - b$$ ?

(A) -2
(B) -1
(C) 0
(D) 2
(E) 4

Source: https://www.gmath.net

ax + b x + b = 2x -1 , for x > 1

a - b = ?

(a+b)x + b = 2x - 1

b = -1, then a+b = 2
a = 3

Now a - b = 3 +1 = 4

E
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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 763
Re: If a and b are constants such that are constants such that ax/(x^2 - 1  [#permalink]

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04 Feb 2019, 13:33
1
fskilnik wrote:
GMATH practice question (Quant Class 13)

If $$a$$ and $$b$$ are constants such that $$\,\,{{ax} \over {{x^2} - 1}} + {b \over {x - 1}} = {{2x - 1} \over {{x^2} - 1}}\,\,$$ for every $$x > 1$$, what is the value of $$a - b$$ ?

(A) -2
(B) -1
(C) 0
(D) 2
(E) 4

Source: https://www.gmath.net

$$? = a - b$$

$${{ax} \over {{x^2} - 1}} + {b \over {x - 1}} = {{2x - 1} \over {{x^2} - 1}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{{ax + b\left( {x + 1} \right)} \over {{x^2} - 1}} = {{2x - 1} \over {{x^2} - 1}}\,\,\,\,\, \Rightarrow \,\,\,\,\,x\left( {a + b - 2} \right) + b + 1 = 0\,\,,\,\,{\rm{for}}\,\,{\rm{all}}\,\,x > 1\,\,\,\,\left( * \right)$$

$$\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,b + 1 = 0\,\,\,\, \Rightarrow \,\,\,\,b = - 1 \hfill \cr \,a + b - 2 = 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a = 3\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 4$$

The correct answer is therefore (E).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Re: If a and b are constants such that are constants such that ax/(x^2 - 1   [#permalink] 04 Feb 2019, 13:33
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