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

Solution; - 4 / t + 1

Step-by-step 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

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.