I have two questions, if any help is given I'd appreciate it.
Simplify using the laws of exponents.
1) (3t - 2t^(-1)) / t^3
2) (3p^2 - p^(-3)) / p^4
Thank you very much.
So my final answers were:
(3t - 2t^(-1)) / t^3
= 3t / t^3 - 2t^(-1)/t^3
= 3t^(1-3) - 2t^(-1-3)
= 3t^(-2) - 2t^(-4)
= (3/t^2) - (2/t^4)
= (3t^2 - 2)/t^4
Is that correct?
(3p^2 - p^(-3))/p^4
= 3p^(2-4) - p^(-3-4)
= 3p^(-2) - p^(-7)
= (3/p^2) - (1/p^7)
= (3p^5 - 1) / p^7
Is that correct?
Notice that the top is the difference of two squares in terms of $\displaystyle \sqrt {x}$
$\displaystyle \frac {x - 9}{x^{1/2} - 3} = \frac {\left( \sqrt {x} \right)^2 - 3^2}{\sqrt {x} - 3}$
$\displaystyle = \frac { \left( \sqrt {x} + 3 \right) \left( \sqrt {x} - 3 \right)}{\sqrt {x} - 3}$
Hopefully the last line is obvious to you
Note that $\displaystyle \frac {x - 1}{ \sqrt {x} - x} = \frac {x - 1}{x \left( x^{-1/2} - 1 \right)}$2) (x-1)/((square root)x - x)
how do you think you should proceed?
Hint: You do the same trick with the top as I did in the last question