Question

Simplify using any method

Answer 1

(t-3)/(t+2)

Explanation:

1 - 2/(t+3)

-------------------

2/(t^2-9) +t/(t-3)

Factor the denominator

1 - 2/(t+3)

-------------------

2/(t-3)(t+3) +t/(t-3)

Multiply the top and bottom bottom by (t-3)(t+3)/ (t-3)(t+3) to clear the fraction

( 1 - 2/(t+3)) * (t-3)(t+3)

-------------------

2/(t-3)(t+3) +t/(t-3) * (t-3)(t+3)

(t-3)(t+3) - 2(t-3)

-------------------

2 +t(t+3)

Distribute

t^2-3t+3t-9 - 2t+6

-------------------

2 +t^2+3t

Combine like terms

t^2-2t-3

-------------------

t^2+3t+2

Factor

(t-3) (t+1)

-------------------

(t+2) (t+1)

Cancel like terms

(t-3)

-------------------

(t+2)