t-10t2-t-6-t+5t2+3t+2

Factor t2-t-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.

-3,2

Write the factored form using these integers.

t-10(t-3)(t+2)-t+5t2+3t+2

t-10(t-3)(t+2)-t+5t2+3t+2

Factor t2+3t+2 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 2 and whose sum is 3.

1,2

Write the factored form using these integers.

t-10(t-3)(t+2)-t+5(t+1)(t+2)

t-10(t-3)(t+2)-t+5(t+1)(t+2)

t-10(t-3)(t+2)-t+5(t+1)(t+2)

To write t-10(t-3)(t+2) as a fraction with a common denominator, multiply by t+1t+1.

t-10(t-3)(t+2)⋅t+1t+1-t+5(t+1)(t+2)

To write -t+5(t+1)(t+2) as a fraction with a common denominator, multiply by t-3t-3.

t-10(t-3)(t+2)⋅t+1t+1-t+5(t+1)(t+2)⋅t-3t-3

Multiply t-10(t-3)(t+2) and t+1t+1.

(t-10)(t+1)(t-3)(t+2)(t+1)-t+5(t+1)(t+2)⋅t-3t-3

Multiply t+5(t+1)(t+2) and t-3t-3.

(t-10)(t+1)(t-3)(t+2)(t+1)-(t+5)(t-3)(t+1)(t+2)(t-3)

Reorder the factors of (t-3)(t+2)(t+1).

(t-10)(t+1)(t+1)(t+2)(t-3)-(t+5)(t-3)(t+1)(t+2)(t-3)

(t-10)(t+1)(t+1)(t+2)(t-3)-(t+5)(t-3)(t+1)(t+2)(t-3)

Combine the numerators over the common denominator.

(t-10)(t+1)-(t+5)(t-3)(t+1)(t+2)(t-3)

Expand (t-10)(t+1) using the FOIL Method.

Apply the distributive property.

t(t+1)-10(t+1)-(t+5)(t-3)(t+1)(t+2)(t-3)

Apply the distributive property.

t⋅t+t⋅1-10(t+1)-(t+5)(t-3)(t+1)(t+2)(t-3)

Apply the distributive property.

t⋅t+t⋅1-10t-10⋅1-(t+5)(t-3)(t+1)(t+2)(t-3)

t⋅t+t⋅1-10t-10⋅1-(t+5)(t-3)(t+1)(t+2)(t-3)

Simplify and combine like terms.

Simplify each term.

Multiply t by t.

t2+t⋅1-10t-10⋅1-(t+5)(t-3)(t+1)(t+2)(t-3)

Multiply t by 1.

t2+t-10t-10⋅1-(t+5)(t-3)(t+1)(t+2)(t-3)

Multiply -10 by 1.

t2+t-10t-10-(t+5)(t-3)(t+1)(t+2)(t-3)

t2+t-10t-10-(t+5)(t-3)(t+1)(t+2)(t-3)

Subtract 10t from t.

t2-9t-10-(t+5)(t-3)(t+1)(t+2)(t-3)

t2-9t-10-(t+5)(t-3)(t+1)(t+2)(t-3)

Apply the distributive property.

t2-9t-10+(-t-1⋅5)(t-3)(t+1)(t+2)(t-3)

Multiply -1 by 5.

t2-9t-10+(-t-5)(t-3)(t+1)(t+2)(t-3)

Expand (-t-5)(t-3) using the FOIL Method.

Apply the distributive property.

t2-9t-10-t(t-3)-5(t-3)(t+1)(t+2)(t-3)

Apply the distributive property.

t2-9t-10-t⋅t-t⋅-3-5(t-3)(t+1)(t+2)(t-3)

Apply the distributive property.

t2-9t-10-t⋅t-t⋅-3-5t-5⋅-3(t+1)(t+2)(t-3)

t2-9t-10-t⋅t-t⋅-3-5t-5⋅-3(t+1)(t+2)(t-3)

Simplify and combine like terms.

Simplify each term.

Multiply t by t by adding the exponents.

Move t.

t2-9t-10-(t⋅t)-t⋅-3-5t-5⋅-3(t+1)(t+2)(t-3)

Multiply t by t.

t2-9t-10-t2-t⋅-3-5t-5⋅-3(t+1)(t+2)(t-3)

t2-9t-10-t2-t⋅-3-5t-5⋅-3(t+1)(t+2)(t-3)

Multiply -3 by -1.

t2-9t-10-t2+3t-5t-5⋅-3(t+1)(t+2)(t-3)

Multiply -5 by -3.

t2-9t-10-t2+3t-5t+15(t+1)(t+2)(t-3)

t2-9t-10-t2+3t-5t+15(t+1)(t+2)(t-3)

Subtract 5t from 3t.

t2-9t-10-t2-2t+15(t+1)(t+2)(t-3)

t2-9t-10-t2-2t+15(t+1)(t+2)(t-3)

Subtract t2 from t2.

-9t-10+0-2t+15(t+1)(t+2)(t-3)

Add -9t and 0.

-9t-10-2t+15(t+1)(t+2)(t-3)

Subtract 2t from -9t.

-11t-10+15(t+1)(t+2)(t-3)

Add -10 and 15.

-11t+5(t+1)(t+2)(t-3)

-11t+5(t+1)(t+2)(t-3)

Factor -1 out of -11t.

-(11t)+5(t+1)(t+2)(t-3)

Rewrite 5 as -1(-5).

-(11t)-1(-5)(t+1)(t+2)(t-3)

Factor -1 out of -(11t)-1(-5).

-(11t-5)(t+1)(t+2)(t-3)

Simplify the expression.

Rewrite -(11t-5) as -1(11t-5).

-1(11t-5)(t+1)(t+2)(t-3)

Move the negative in front of the fraction.

-11t-5(t+1)(t+2)(t-3)

-11t-5(t+1)(t+2)(t-3)

-11t-5(t+1)(t+2)(t-3)

Combine (t-10)/(t^2-t-6)-(t+5)/(t^2+3t+2)