Divide and simplify,if possible

Question

Divide and simplify if possible 

 

3x+12 ÷ (x+4)^2

4x_12     (x-3)^2

Answer 1

((3x+12)/(4x-12))/(((x+4)^2)/((x-3)^2))

 

No Division by Zero Constraints: x ≠ 3, -4

 

Change division by fraction to multiplication by its reciprocal:

 

((3x+12)/(4x-12))*(((x-3)^2)/((x+4)^2))

 

Take out Greatest Common Factors:

 

(3(x+4)/(4(x-3)))*(((x-3)^2)/((x+4)^2))

 

Multiply Fractions:

 

(3(x+4)(x-3)^2)/(4(x-3)(x+4)^2)

 

Factor Common Factors out of Numerator and Denominator:

 

(3(x-3))/(4(x+4))*((x+4)/(x+4))*((x-3)/(x-3))

 

Iff x ≠ 3, -4 then ((x+4)/(x+4))*((x-3)/(x-3)) = 1; otherwise it's UNDEFINED.

 

["Iff" means "If and only if".]

 

(3(x-3))/(4(x+4))*1, x ≠ 3, -4

 

(3/4)*(x-3)/(x+4), x ≠ 3, -4

Answer 2

Hi Theresa,

 

3x+12 ÷(x+4)²

4x-12     (x-3)²

 

3(x+4) ×(x-3)²

4(x-3)     (x+4)²

 

3(x-3)

4(x+4)

 

For x=-4 and x =3 the solution is not defined.