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Question

Answer 1

The given equation ( x²+6x + 8 / x²-16) / ( x²+7x+10/ x²-25)

 x²+6x + 8 =  x²+2x +4x +8  = 0

=  x( x+2) +4( x+2) = 0

= ( x+2) ( x+4)

x²+7x+10 = x²+ 2x +5x + 10 = 0

= x( x+2) +5( x+2) = 0

= ( x+2) (x+5)

Therefore { [ (x+2)(x+4)] / (x-4)(x+4)}  / { [ (x+2)(x+5)] / (x-5)(x+5)}

= [ (x+2) /(x-4)] / [(x+2)/(x-5) ]

= [ (x+2)/(x-4)] [(x-5)/(x+2)]

= (x-4)/(x-5).

Therefore the  fraction  obtained is  ( x-4)(x-5).

Comments

= [ (x+2)/(x-4)] [(x-5)/(x+2)]

= (x-5)/(x-4).

Therefore, the fraction obtained is (x-5)/(x-4).