Question

x^2-4x-5 over x^2-9 divided by x^2-x-2 over x^2-4x+3 ??? divide and simplify

Answer 1

X^2-4X-5/X^2-9/X^2-X-2/X^2-4x+3
=>x^2-5x+x-5/x^2-9/x^2-2x+x-2/x^2-3x-x+3
=>x(x-5)+1(x-5)/x^2-9/x(x-2)+1(x-2)/x(x-3)+1(x-3)
=>(x-5)(x+1)/x^2-9/(x-2)(x+1)/(x-3)(x+1)
=>(x-5)(x+1)/(x+3)(x-3).(x-3)/(x-2)
=>(x-5)(x+1)/(x+3)(x-2)

Answer 2

\[\frac{x^2-4x-5}{x^2-9} \div \frac{x^2-x-2}{x^2-4x+3}\]
\[\frac{x^2-5x+x-5}{(x+3)(x-3)} \div \frac{x^2-2+xx-2}{x^2-3x-x+3}\]
\[\frac{x(x-5)+1(x-5)}{(x+3)(x-3)} \div \frac{x(x-2)+1(x-2)}{x(x-3)-1(x-3)}\]
\[\frac{(x+1)(x-5)}{(x+3)(x-3)} \div \frac{(x+1)(x-2)}{(x-1)(x-3)}\]
\[\frac{(x+1)(x-5)}{(x+3)(x-3)} \times \frac{(x-1)(x-3)}{(x+1)(x-2)}\]
\[\frac{(x-5)}{(x+3)} \times \frac{(x-1)}{(x-2)}=\frac{(x-5)(x-1)}{(x+3)(x-2)}\]