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y = [tex]\frac{a+w}{a-w}[/tex]); solve for w

the answer is w = [tex]\frac{a(y-1)}{y+1}[/tex]); a ≠ w, y ≠ 1

I know the answer but I'd like to know how to get the answer please.

Respuesta :

LammettHash

Multiply both sides by [tex]a-w[/tex]:

[tex]y(a-w)=\dfrac{(a+w)(a-w)}{a-w}[/tex]

Then as long as [tex]a\neq w[/tex], we can cancel both factors of [tex]a-w[/tex] on the right:

[tex]y(a-w)=a+w[/tex]

Distribute the [tex]y[/tex] on the left side:

[tex]ya-yw=a+w[/tex]

and group all the terms containing [tex]w[/tex] on one side:

[tex]yw+w=ya-a[/tex]

We can factorize both sides:

[tex]w(y+1)=a(y-1)[/tex]

then divide both sides by [tex]y+1[/tex] and solve for [tex]w[/tex]:

[tex]w=\dfrac{a(y-1)}{y+1}[/tex]

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