23×2+4x-7+13×2+19x+28

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-7=-21 and whose sum is b=4.

Factor 4 out of 4x.

23×2+4(x)-7+13×2+19x+28

Rewrite 4 as -3 plus 7

23×2+(-3+7)x-7+13×2+19x+28

Apply the distributive property.

23×2-3x+7x-7+13×2+19x+28

23×2-3x+7x-7+13×2+19x+28

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2(3×2-3x)+7x-7+13×2+19x+28

Factor out the greatest common factor (GCF) from each group.

23x(x-1)+7(x-1)+13×2+19x+28

23x(x-1)+7(x-1)+13×2+19x+28

Factor the polynomial by factoring out the greatest common factor, x-1.

2(x-1)(3x+7)+13×2+19x+28

2(x-1)(3x+7)+13×2+19x+28

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅28=84 and whose sum is b=19.

Factor 19 out of 19x.

2(x-1)(3x+7)+13×2+19(x)+28

Rewrite 19 as 7 plus 12

2(x-1)(3x+7)+13×2+(7+12)x+28

Apply the distributive property.

2(x-1)(3x+7)+13×2+7x+12x+28

2(x-1)(3x+7)+13×2+7x+12x+28

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2(x-1)(3x+7)+1(3×2+7x)+12x+28

Factor out the greatest common factor (GCF) from each group.

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

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

Factor the polynomial by factoring out the greatest common factor, 3x+7.

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

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

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

To write 2(x-1)(3x+7) as a fraction with a common denominator, multiply by x+4x+4.

2(x-1)(3x+7)⋅x+4x+4+1(3x+7)(x+4)

To write 1(3x+7)(x+4) as a fraction with a common denominator, multiply by x-1x-1.

2(x-1)(3x+7)⋅x+4x+4+1(3x+7)(x+4)⋅x-1x-1

Multiply 2(x-1)(3x+7) and x+4x+4.

2(x+4)(x-1)(3x+7)(x+4)+1(3x+7)(x+4)⋅x-1x-1

Multiply 1(3x+7)(x+4) and x-1x-1.

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

Reorder the factors of (x-1)(3x+7)(x+4).

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

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

Combine the numerators over the common denominator.

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

Apply the distributive property.

2x+2⋅4+x-1(3x+7)(x+4)(x-1)

Multiply 2 by 4.

2x+8+x-1(3x+7)(x+4)(x-1)

Add 2x and x.

3x+8-1(3x+7)(x+4)(x-1)

Subtract 1 from 8.

3x+7(3x+7)(x+4)(x-1)

3x+7(3x+7)(x+4)(x-1)

Cancel the common factor.

3x+7(3x+7)(x+4)(x-1)

Rewrite the expression.

1(x+4)(x-1)

1(x+4)(x-1)

Simplify 2/(3x^2+4x-7)+1/(3x^2+19x+28)