x+1×2+6x+9+x-4×2-9

Factor using the perfect square rule.

Rewrite 9 as 32.

x+1×2+6x+32+x-4×2-9

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

6x=2⋅x⋅3

Rewrite the polynomial.

x+1×2+2⋅x⋅3+32+x-4×2-9

Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=x and b=3.

x+1(x+3)2+x-4×2-9

x+1(x+3)2+x-4×2-9

Simplify the denominator.

Rewrite 9 as 32.

x+1(x+3)2+x-4×2-32

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=3.

x+1(x+3)2+x-4(x+3)(x-3)

x+1(x+3)2+x-4(x+3)(x-3)

x+1(x+3)2+x-4(x+3)(x-3)

To write x+1(x+3)2 as a fraction with a common denominator, multiply by x-3x-3.

x+1(x+3)2⋅x-3x-3+x-4(x+3)(x-3)

To write x-4(x+3)(x-3) as a fraction with a common denominator, multiply by x+3x+3.

x+1(x+3)2⋅x-3x-3+x-4(x+3)(x-3)⋅x+3x+3

Multiply x+1(x+3)2 and x-3x-3.

(x+1)(x-3)(x+3)2(x-3)+x-4(x+3)(x-3)⋅x+3x+3

Multiply x-4(x+3)(x-3) and x+3x+3.

(x+1)(x-3)(x+3)2(x-3)+(x-4)(x+3)(x+3)(x-3)(x+3)

Raise x+3 to the power of 1.

(x+1)(x-3)(x+3)2(x-3)+(x-4)(x+3)(x+3)1(x+3)(x-3)

Raise x+3 to the power of 1.

(x+1)(x-3)(x+3)2(x-3)+(x-4)(x+3)(x+3)1(x+3)1(x-3)

Use the power rule aman=am+n to combine exponents.

(x+1)(x-3)(x+3)2(x-3)+(x-4)(x+3)(x+3)1+1(x-3)

Add 1 and 1.

(x+1)(x-3)(x+3)2(x-3)+(x-4)(x+3)(x+3)2(x-3)

(x+1)(x-3)(x+3)2(x-3)+(x-4)(x+3)(x+3)2(x-3)

Combine the numerators over the common denominator.

(x+1)(x-3)+(x-4)(x+3)(x+3)2(x-3)

Expand (x+1)(x-3) using the FOIL Method.

Apply the distributive property.

x(x-3)+1(x-3)+(x-4)(x+3)(x+3)2(x-3)

Apply the distributive property.

x⋅x+x⋅-3+1(x-3)+(x-4)(x+3)(x+3)2(x-3)

Apply the distributive property.

x⋅x+x⋅-3+1x+1⋅-3+(x-4)(x+3)(x+3)2(x-3)

x⋅x+x⋅-3+1x+1⋅-3+(x-4)(x+3)(x+3)2(x-3)

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2+x⋅-3+1x+1⋅-3+(x-4)(x+3)(x+3)2(x-3)

Move -3 to the left of x.

x2-3⋅x+1x+1⋅-3+(x-4)(x+3)(x+3)2(x-3)

Multiply x by 1.

x2-3x+x+1⋅-3+(x-4)(x+3)(x+3)2(x-3)

Multiply -3 by 1.

x2-3x+x-3+(x-4)(x+3)(x+3)2(x-3)

x2-3x+x-3+(x-4)(x+3)(x+3)2(x-3)

Add -3x and x.

x2-2x-3+(x-4)(x+3)(x+3)2(x-3)

x2-2x-3+(x-4)(x+3)(x+3)2(x-3)

Expand (x-4)(x+3) using the FOIL Method.

Apply the distributive property.

x2-2x-3+x(x+3)-4(x+3)(x+3)2(x-3)

Apply the distributive property.

x2-2x-3+x⋅x+x⋅3-4(x+3)(x+3)2(x-3)

Apply the distributive property.

x2-2x-3+x⋅x+x⋅3-4x-4⋅3(x+3)2(x-3)

x2-2x-3+x⋅x+x⋅3-4x-4⋅3(x+3)2(x-3)

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2-2x-3+x2+x⋅3-4x-4⋅3(x+3)2(x-3)

Move 3 to the left of x.

x2-2x-3+x2+3⋅x-4x-4⋅3(x+3)2(x-3)

Multiply -4 by 3.

x2-2x-3+x2+3x-4x-12(x+3)2(x-3)

x2-2x-3+x2+3x-4x-12(x+3)2(x-3)

Subtract 4x from 3x.

x2-2x-3+x2-x-12(x+3)2(x-3)

x2-2x-3+x2-x-12(x+3)2(x-3)

Add x2 and x2.

2×2-2x-3-x-12(x+3)2(x-3)

Subtract x from -2x.

2×2-3x-3-12(x+3)2(x-3)

Subtract 12 from -3.

2×2-3x-15(x+3)2(x-3)

2×2-3x-15(x+3)2(x-3)

Add (x+1)/(x^2+6x+9)+(x-4)/(x^2-9)