Q&A Bank q 1.29 - rearranging?

[12345]

Hello all,

Could anyone provide a stepped solution as to how this is rearranged from this:

1/w = p(1/w1) + (1-p)(1/w2)

to

w1w2 = w[p(w2)+(1-p)(w1)]

and then to

w = (w1w2)/(p(w2)+(1-p)(w1))

Any takers?

 

[Little Miss Actuary]

1/w = p(1/w1) + (1-p)(1/w2)

Multiply both sides by w1w2:

w1w2/w = p(w1w2/w1) + (1-p)(w1w2/w2)
w1w2/w = p(w2)+(1-p)(w1)

Multiply both side by w:

w1w2 = w[p(w2)+(1-p)(w1)]

Divide both sides by [p(w2)+(1-p)(w1)]:

w = (w1w2)/[p(w2)+(1-p)(w1)]

 

[12345]

Fantastic, much obliged.