Question

What is the simplified form of (12-4t)/(t^2-2t-3)? State any excluded values

Answer 1

Solution; - 4 / t + 1

Explanation:

See procedure below;

( 12 - 4t ) / ( t^2 - 2t - 3 ) ⇒ Factor out common term - 4 in 12 - 4t,

- 4 * ( t - 3 ) / ( t^2 - 2t - 3 ) ⇒ Break bottom expression into groups,

- 4 * ( t - 3 ) / ( t^2 + t ) + ( - 3t - 3 ) ⇒ Factor out t from t^2 + t,

- 4 * ( t - 3 ) / t * ( t + 1 ) + ( - 3t - 3 ) ⇒ Factor out - 3 from - 3t - 3,

- 4 * ( t - 3 ) / t * ( t + 1 ) + ( - 3 * ( t + 1 ) ) ⇒ Factor out common term t + 1,

- 4 * ( t - 3 ) / ( t + 1 ) * ( t - 3 ) ⇒ Cancel out like term t - 3,

Solution; - 4 / t + 1