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Question

 

simplify, whats the non permissible and the show how to check the answer.

 

b)  4x-1 over x²+7x+12 Divided by 2x-6 over x²+x-12

 

Answer 1

Given expression is

 

Convert binomial expressions into factorized form.

x² + 7x + 12 = x² + 4x +3x + 12 = x(x+4)+3(x+4) = (x+4)(x+3)

x² + x - 12 = x² + 4x -3x - 12 = x(x+4)-3(x+4) = (x+4)(x-3)

Substitute x² + 7x + 12 = (x+4)(x+3)  and x² + x - 12 = (x+4)(x-3) in the above expression.

Non permissible value : It is the value of the variable in the rational expression that which makes the rational expression undefined.To find Non permissible value make denominator equals to zero.

2 ( x + 3 ) = 0

x + 3 = 0

x = - 3.

Non permissible value : x = - 3.

 

Checking of the the simplified answer :

Substitute test value x = 1

Both sides are equal. So simplified answer is verified.

Checking of the the Non permissible value  :

Substitute non permissible value x = -3 in the given expression.

So non permissible value also verified.