Question

I need help understanding how to cross-multiply addition of inverse functions. I'm given this,

1/p+1/(p-45) = 1/30

The answer goes to p^2-105p+1,350 = 0.

My method has been adjusting the ratios of the numerator and denominators to give,

[30(p-45)]/[30p(p-45)]+[30p]/[30p(p-45)] = [p(p-45)]/[30p(p-45)]

I add the like denominators on the left, and then cross multiply in order to cancel the [30p(p-45)] term.

1 = p(p-45)/1,350 ==> p^2-45p+1,350 = 0

How is my professor getting -105p instead of -45p?

Thanks

Answer 1

how about we multiply the entire equation
1/p+1/(p-45) = 1/30
by
30p(p-45)

30(p-45) +30p = p(p-45)

30 p - 1350 + 30 p = p^2 -45 p

p^2 -(45+30+30)p + 1350 = 0

p^2 - 105 p + 1350 = 0