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# Divide and simplify,if possible

Divide and simplify if possible

3x+12 ÷ (x+4)^2
4x_12     (x-3)^2

### 2 Answers by Expert Tutors

Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
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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.

Try putting x = 3 into the original equation.
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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((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