Write the rational expression as an equivalent rational expression in lowest terms ((x-3)/(x²-4)). ((x²-x-6)/(x-2)).

Answer:The lowest form of the fraction is [tex](\frac{x-3}{x-2} )^{2}[/tex]Step-by-step explanation:Here, the given equation is [tex]\frac{(x-3)}{(x^{2} -4)} \times \frac{(x^{2} - x - 6) }{(x-2)}[/tex]Now, by ALGEBRAIC IDENTITIES, we know that:[tex]a^{2} - b^{2}  = (a-b)(a+b)[/tex]Here, [tex]( x^{2} -4) = (x^{2}  - (2)^{2} ) = (x-2)(x+2)[/tex]Also, [tex]x^{2} - x -6 = (x-3)(x+2)[/tex] (by splitting the middle term)So, the given expression becomes:[tex]\frac{(x-3)}{(x^{2} -4)} \times \frac{(x^{2} - x - 6) }{(x-2)}[/tex]  = [tex]\frac{(x-3)}{(x-2)(x+ 2)} \times \frac{(x-3)(x+2) }{(x-2)}[/tex]or, the expression becomes [tex]\frac{(x-3)}{(x-2)(x+ 2)} \times \frac{(x-3)(x+2) }{(x-2)}[/tex]= [tex]\frac{(x-3)^{2} }{(x-2)^{2} }  = (\frac{x-3}{x-2} )^{2}[/tex]So,the lowest form of the fraction is [tex](\frac{x-3}{x-2} )^{2}[/tex]