y2-13y2-2y-3-13-y

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 -3 and whose sum is -2.

-3,1

Write the factored form using these integers.

y2-13(y-3)(y+1)-13-y

y2-13(y-3)(y+1)-13-y

Rewrite 3 as -1(-3).

y2-13(y-3)(y+1)-1-1(-3)-y

Factor -1 out of -y.

y2-13(y-3)(y+1)-1-1(-3)-(y)

Factor -1 out of -1(-3)-(y).

y2-13(y-3)(y+1)-1-1(-3+y)

Reorder terms.

y2-13(y-3)(y+1)-1-1(y-3)

y2-13(y-3)(y+1)-1-1(y-3)

To write y2-13(y-3)(y+1) as a fraction with a common denominator, multiply by -1-1.

y2-13(y-3)(y+1)⋅-1-1-1-1(y-3)

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

y2-13(y-3)(y+1)⋅-1-1-1-1(y-3)⋅y+1y+1

Multiply y2-13(y-3)(y+1) and -1-1.

(y2-13)⋅-1(y-3)(y+1)⋅-1-1-1(y-3)⋅y+1y+1

Multiply 1-1(y-3) and y+1y+1.

(y2-13)⋅-1(y-3)(y+1)⋅-1-y+1-1(y-3)(y+1)

Reorder the factors of (y-3)(y+1)⋅-1.

(y2-13)⋅-1-(y+1)(y-3)-y+1-1(y-3)(y+1)

Reorder the factors of -1(y-3)(y+1).

(y2-13)⋅-1-(y+1)(y-3)-y+1-(y+1)(y-3)

(y2-13)⋅-1-(y+1)(y-3)-y+1-(y+1)(y-3)

Combine the numerators over the common denominator.

(y2-13)⋅-1-(y+1)-(y+1)(y-3)

Apply the distributive property.

y2⋅-1-13⋅-1-(y+1)-(y+1)(y-3)

Move -1 to the left of y2.

-1⋅y2-13⋅-1-(y+1)-(y+1)(y-3)

Multiply -13 by -1.

-1⋅y2+13-(y+1)-(y+1)(y-3)

Rewrite -1y2 as -y2.

-y2+13-(y+1)-(y+1)(y-3)

Apply the distributive property.

-y2+13-y-1⋅1-(y+1)(y-3)

Multiply -1 by 1.

-y2+13-y-1-(y+1)(y-3)

Subtract 1 from 13.

-y2-y+12-(y+1)(y-3)

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=-1⋅12=-12 and whose sum is b=-1.

Factor -1 out of -y.

-y2-(y)+12-(y+1)(y-3)

Rewrite -1 as 3 plus -4

-y2+(3-4)y+12-(y+1)(y-3)

Apply the distributive property.

-y2+3y-4y+12-(y+1)(y-3)

-y2+3y-4y+12-(y+1)(y-3)

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(-y2+3y)-4y+12-(y+1)(y-3)

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

y(-y+3)+4(-y+3)-(y+1)(y-3)

y(-y+3)+4(-y+3)-(y+1)(y-3)

Factor the polynomial by factoring out the greatest common factor, -y+3.

(-y+3)(y+4)-(y+1)(y-3)

(-y+3)(y+4)-(y+1)(y-3)

(-y+3)(y+4)-(y+1)(y-3)

Cancel the common factor of -y+3 and y-3.

Factor -1 out of -y.

(-(y)+3)(y+4)-(y+1)(y-3)

Rewrite 3 as -1(-3).

(-(y)-1(-3))(y+4)-(y+1)(y-3)

Factor -1 out of -(y)-1(-3).

-(y-3)(y+4)-(y+1)(y-3)

Rewrite -(y-3) as -1(y-3).

-1(y-3)(y+4)-(y+1)(y-3)

Cancel the common factor.

-1(y-3)(y+4)-(y+1)(y-3)

Rewrite the expression.

-1(y+4)-(y+1)

-1(y+4)-(y+1)

Dividing two negative values results in a positive value.

y+4y+1

y+4y+1

Combine (y^2-13)/(y^2-2y-3)-1/(3-y)