Question

I need help with this math problem

Answer 1

1).
`(2)/(x^(2)-x-12 )=(2)/((x+3)(x-4))`

2).
`(1)/(x^(2)-16 )=(1)/((x-4)(x+4))`

Explanation:

In this question we have to write the fractions in the factored form.

Rational expressions are
`(2)/(x^(2)-x-12 )` and
`(1)/(x^(2)-16 )`.

1).
`(2)/(x^(2)-x-12 )`

Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12

= x(x - 4) + 3(x - 4)

= (x + 3)(x - 4)

Therefore.
`(2)/(x^(2)-x-12 )=(2)/((x+3)(x-4))`

2).
`(1)/(x^(2)-16 )`

Factored form of the denominator (x² - 16) = (x - 4)(x + 4)

[Since (a²- b²) = (a - b)(a + b)]

Therefore,
`(1)/(x^(2)-16 )=(1)/((x-4)(x+4))`