Question

How do you evaluate `(x-6)/(x-4) +( 3x +4) / (-3x -3)`?

Answer 1

`-((7x + 2)/(3x^2 - 9x - 12))`

Explanation:

`(x - 6)/(x - 4) + (3x + 4)/(-3x - 3)` = `(-3(x+1)(x-6)+ (3x +4)(x -4))/(-3(x-4)(x +1))`

= `((-3x^2+15x +18) + (3x^2 -8x -16))/(-3x^2 + 9x +12)`

= `-((7x + 2)/(3x^2 - 9x - 12))`

Answer 2

`-(7x+2)/(3(x-4)(x+1)`

Explanation:

`"before adding the fractions we require them to have a"`
`color(blue)"common denominator"`

`"the "color(blue)"common denominator ""is "(x-4)(-3x-3)`

`"multiply the numerators/denominators by the appropriate"`
`"factor to obtain common denominator"`

`(x-6)/(x-4)xx(-3x-3)/(-3x-3)+(3x+4)/(-3x+3)xx(x-4)/(x-4)`

`=((x-6)(-3x-3))/((x-4)(-3x-3))+((3x+4)(x-4))/((x-4)(-3x-3))`

`"expand and simplify numerator leaving the denominator"`

`=(cancel(-3x^2)+15x+18cancel(+3x^2)-8x-16)/((x-4)(-3x-3))`

`=(7x+2)/(-3(x-4)(x+1))larr"common factor of "-3`

`=-(7x+2)/(3(x-4)(x+1))`