Simplify (x+9)/(x-2)+(-8x-39)/(x^2+x-6)

x+9x-2+-8x-39×2+x-6
Factor x2+x-6 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is 1.
-2,3
Write the factored form using these integers.
x+9x-2+-8x-39(x-2)(x+3)
x+9x-2+-8x-39(x-2)(x+3)
To write x+9x-2 as a fraction with a common denominator, multiply by x+3x+3.
x+9x-2⋅x+3x+3+-8x-39(x-2)(x+3)
Simplify terms.
Multiply x+9x-2 and x+3x+3.
(x+9)(x+3)(x-2)(x+3)+-8x-39(x-2)(x+3)
Combine the numerators over the common denominator.
(x+9)(x+3)-8x-39(x-2)(x+3)
(x+9)(x+3)-8x-39(x-2)(x+3)
Simplify the numerator.
Expand (x+9)(x+3) using the FOIL Method.
Apply the distributive property.
x(x+3)+9(x+3)-8x-39(x-2)(x+3)
Apply the distributive property.
x⋅x+x⋅3+9(x+3)-8x-39(x-2)(x+3)
Apply the distributive property.
x⋅x+x⋅3+9x+9⋅3-8x-39(x-2)(x+3)
x⋅x+x⋅3+9x+9⋅3-8x-39(x-2)(x+3)
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
x2+x⋅3+9x+9⋅3-8x-39(x-2)(x+3)
Move 3 to the left of x.
x2+3⋅x+9x+9⋅3-8x-39(x-2)(x+3)
Multiply 9 by 3.
x2+3x+9x+27-8x-39(x-2)(x+3)
x2+3x+9x+27-8x-39(x-2)(x+3)
Add 3x and 9x.
x2+12x+27-8x-39(x-2)(x+3)
x2+12x+27-8x-39(x-2)(x+3)
Subtract 8x from 12x.
x2+4x+27-39(x-2)(x+3)
Subtract 39 from 27.
x2+4x-12(x-2)(x+3)
Factor x2+4x-12 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -12 and whose sum is 4.
-2,6
Write the factored form using these integers.
(x-2)(x+6)(x-2)(x+3)
(x-2)(x+6)(x-2)(x+3)
(x-2)(x+6)(x-2)(x+3)
Cancel the common factor of x-2.
Cancel the common factor.
(x-2)(x+6)(x-2)(x+3)
Rewrite the expression.
x+6x+3
x+6x+3
Simplify (x+9)/(x-2)+(-8x-39)/(x^2+x-6)