x+9x-2+-8x-39×2+x-6

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)

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)

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.

(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)