Question

Subtract need answers now pls

Answer 1

`(2x^2-5x-3)/((x-4)(x+4))`

Explanation:

`(3x-5)/(x-4)` -
`(x^2+12x-17)/(x^2-16)`

before subtracting the fractions we require them to have a common denominator

x² - 16 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 16

= x² - 4²

= (x - 4)(x + 4)

the subtraction now becomes

`(3x-5)/(x-4)` -
`(x^2+12x-17)/((x-4)(x+4))`

multiply the numerator/ denominator of the first fraction by (x + 4)

=
`((3x-5)(x+4))/((x-4)(x+4))` -
`(x^2+12x-17)/((x-4)(x+4))` ← both with common denominator

expand numerator of first fraction using FOIL

=
`(3x^2+7x-20)/((x-4)(x+4))` -
`(x^2+12x-17)/((x-4)(x+4))`

subtract the numerators, over the common denominator

=
`(3x^2+7x-20-(x^2+12x-17))/((x-4)(x+4))`

=
`(3x^2+7x-20-x^2-12x+17)/((x-4)(x+4))` ← collect like terms on numerator

=
`(2x^2-5x-3)/((x-4)(x+4))`