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If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then

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Bunuel
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If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   30 Dec 2019, 13:08
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If \(f(w) =\frac{1}{w} + \frac{1}{w+8}\) and the function f(w) equals \(\frac{1}{w-1}\), then a possible value for w could be

(A) -8
(B) -4
(C) -2
(D) -1
(E) 3
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C
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   30 Dec 2019, 13:45
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1/w + 1/(w+8) = 1/(w-1)

Evaluate available choice:
(A) -8, NO!, because 1/(w+8) =1/0.
(B) -4, NO!, because 1/-4 + 1/(2) = 1/(-5)
(C) -2, Yes!, because 1/-2 + 1/(6) = 1/(-3)

We stop at (C) because we have found the answer.

FINAL ANSWER IS (C)

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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   31 Dec 2019, 04:42
use plug in technique
at w = -2
we get
1/w+1/w+8 = 2w+8/w(w+8) ; -1/3
and
1/w−1 = -1/3
IMO C; -2


If f(w)=1/w+1/w+8 and the function f(w) equals 1/w−1, then a possible value for w could be

(A) -8
(B) -4
(C) -2
(D) -1
(E) 3
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   31 Dec 2019, 06:12
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f(w) = 1/w + 1/(w+8) and f(w)=1/(w-1)
equating both functions of f(w): 1/w + 1/(w+8) = 1/(w-1)
(2w+8)/(w^2 + 8w) = 1/(w-1)
2w^2 - 2w + 8w - 8 = w^2 + 8w
w^2 - 2w -8 =0
(w-4)(w-2)=0
w=4 or w=-2

The answer is C.
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   31 Dec 2019, 06:33
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Quote:
If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1), then a possible value for w could be

(A) -8
(B) -4
(C) -2
(D) -1
(E) 3


1/w + 1/(w + 8) = 1/(w - 1)
2w+8=w(w+8)/(w-1)
w^2-2w-8=0
(w-4)(w+2)=0
w=4,-2

Ans (C)
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   31 Dec 2019, 06:48
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\(\frac{1}{w} + \frac{1}{(w + 8) }= \frac{1}{(w - 1)}\)

On Solving, We get equation:

\(w^2-2w-8 = 0\)

\((w+2)(w-4) = 0\)

\(w = -2\) \(or 4\)

Option C
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   31 Dec 2019, 08:42
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By equating: \(\frac{1}{w}\) + \(\frac{1}{w+8}\) = \(\frac{1}{w-1}\) --> w = 4 and w = -2

Hence correct option is C
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   31 Dec 2019, 09:12
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\(\frac{1}{w}+ \frac{1}{w+8} = \frac{1}{w-1}\)

\(=> \frac{2w+8 }{ w^{2}+8w} = \frac{1}{w-1}\)

\(=> w^{2} + 8w = 2w^{2} + 8w - 2w - 8\)
\(=> w^{2} - 2w - 8 = 0\)
=> w = -2 or w = 4
=> Choice C
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   31 Dec 2019, 10:38
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Putting value of w = -2

1/w + 1/(w+8) = -1/2 + 1/6 = -1/3
1/(w-1) = -1/3

IMO C

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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink] New post   18 Feb 2024, 19:42
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Re: If f(w) = 1/w + 1/(w + 8) and the function f(w) equals 1/(w - 1) then [#permalink]
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