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What is the quotient in simplest form? State any restrictions on the variable. Show all work.

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

What is the quotient in simplest form State any restrictions on the variable Show all work x24x3 divided by x2x2x12 class=

Respuesta :

choixongdong

Answer:

(x-2) (x+4)

Step-by-step explanation:

   (x^2-4)         (x^2+x-12)

= --------------- * ---------------          ; x  ≠3 or x ≠ -2

    (x-3)              (x+2)

  (x+2)(x-2)       (x-3)(x+4)

= --------------- * ---------------

    (x-3)               (x+2)

= (x-2) (x+4)

       

kudzordzifrancis

Answer:

[tex]\frac{z-2}{z+4},z\ne-4[/tex]

Step-by-step explanation:

The given quotient is

[tex]\frac{z^2-4}{z-3}\div \frac{z+2}{z^2+z-12}[/tex]

Multiply by the reciprocal of the second fraction;

[tex]\frac{z^2-4}{z-3}\times \frac{z^2+z-12}{z+2}[/tex]

Factorize the numerators;

[tex]\frac{z^2-2^2}{z-3}\times \frac{z^2+4z-3z-12}{z+2}[/tex]

[tex]\frac{(z-2)(z+2)}{z-3}\times \frac{z(z+4)-3(z+4)}{z+2}[/tex]

[tex]\frac{(z-2)(z+2)}{z-3}\times \frac{(z-3)(z+4)}{z+2}[/tex]

Cancel out the common factors;

[tex]\frac{(z-2)(1)}{1}\times \frac{(1)(z+4)}{1}[/tex]

[tex]\frac{z-2}{z+4},z\ne-4[/tex]

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