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

2 Answers
Dec 31, 2017

-((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))

Dec 31, 2017

-(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))