Question

Perform the indicated operation and simplify the result:


`(x^(2)-6x-16 )/(x^(2)+5x+6)` ÷
`(x^(2) -2x-48)/(x^(2)+x-2 )`
a)
`(x+2)/(x+4)`
b)
`(x-2)/(x+6)`
c)
`(x-2)/(x-4)`
d)
`(x+2)/(x-6)`

Answer 1

To perform the indicated operation and simplify the result of the given expression, we can multiply the first fraction by the reciprocal of the second fraction, factor the numerators and denominators, and then cancel out common factors to simplify the expression. The simplified expression is
`rac{x-1}{x+6}`.

Step-by-step explanation:

To perform the indicated operation and simplify the result:

`rac{x^(2)-6x-16 }{x^(2)+5x+6}` ÷
`rac{x^(2) -2x-48}{x^(2)+x-2 }`

We can start by multiplying the first fraction by the reciprocal of the second fraction:

`rac{x^(2)-6x-16 }{x^(2)+5x+6}` ÷
`rac{x^(2) -2x-48}{x^(2)+x-2 }` =
`rac{x^(2)-6x-16 }{x^(2)+5x+6}` ×
`rac{x^(2)+x-2}{x^(2) -2x-48}`

We can factor the numerators and denominators of the fractions to simplify:

`rac{(x-8)(x+2) }{(x+3)(x+2)}` ×
`rac{(x+2)(x-1)}{(x-8)(x+6)}`

Now we can cancel out the common factors and simplify the expression:

`rac{(x-8)(x+2) }{(x+3)(x+2)}` ×
`rac{(x+2)(x-1)}{(x-8)(x+6)}` =
`rac{x-1}{x+6}`