Question

How do I put this rational expression in simplest form? Steps please!!!!

Answer 1

4.
b^-2-x^-2/b^-1+x^-1

b^-2/b^-1=b^-1
x^-2/x^-1=x^-1
As a result, the simplest form is:
b^-1-x^-1. Hope it help!

Answer 2

$\bf a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}}\\\\ -----------------------------\\\\ \cfrac{b^{-2}-x^{-2}}{b^{-1}-x^{-1}}\implies \cfrac{\frac{1}{b^2}-\frac{1}{x^2}}{\frac{1}{b}+\frac{1}{x}}\implies \cfrac{\frac{x^2-b^2}{b^2x^2}}{\frac{x+b}{bx}}\implies \cfrac{x^2-b^2}{b^2x^2}\cdot \cfrac{bx}{x+b}$

$\bf -----------------------------\\\\ \textit{now recall your }\textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -----------------------------\\\\ \cfrac{(x-b)\underline{(x+b)}}{\underline{(bx)^2}}\cdot \cfrac{\underline{bx}}{\underline{x+b}}\implies \cfrac{x-b}{bx}$