How do I solve this

Mathematics

1 answer:

sdas [7]3 years ago

3 0

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\
\cfrac{2x}{x^2+2x-24}-\cfrac{x}{x^2-36}\quad 
\begin{cases}
x^2+2x-24\implies (x+6)(x-4)\\
--------------\\
x^2-36\implies x^2-6^2\\
(x-6)(x+6)
\end{cases}$

$\bf \cfrac{2x}{(x+6)(x-4)}-\cfrac{x}{(x-6)(x+6)}\impliedby 
\begin{array}{llll}
\textit{thus our LCD is}\\
(x-6)(x+6)(x-4)
\end{array}
\\\\\\
\cfrac{[(x-6)2x]~-~[(x-4)x]}{(x-6)(x+6)(x-4)}\implies \cfrac{2x^2-12x-x^2+4x}{(x-6)(x+6)(x-4)}
\\\\\\
\cfrac{x^2-8x}{(x-6)(x+6)(x-4)}$

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