Make 'n' the subject of the formula if w = \(\frac{v(2 + cn)}{1 - cn}\)

Mathematics

JAMB 2012

A. \(\frac{1}{c}(\frac{w - 2v}{v + w})\)
B. \(\frac{1}{c}(\frac{w - 2v}{v - w})\)
C. \(\frac{1}{c}(\frac{w + 2v}{v - w})\)
D. \(\frac{1}{c}(\frac{w + 2v}{v + w})\)

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Correct Answer: Option A

Explanation

w = \(\frac{v(2 + cn)}{1 - cn}\)

2v + cnv = w(1 - cn)

2v + cnv = w - cnw

2v - w = -cnv - cnw

Multiply through by negative sign

-2v + w = cnv + cnw

-2v + w = n(cv + cw)

n = \(\frac{-2v + w}{cv + cw}\)

n = \(\frac{1}{c}\frac{-2v + w}{v + w}\)

Re-arrange...

n = \(\frac{1}{c}\frac{w - 2v}{v + w}\)

There is an explanation video available below.

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