Question

Divide. Express the quotient in simplest form. (x^2−x−12)/(2x^2)÷(x^2+x−6)/2x^3

Answer 1

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Answer 2

$(x^2−x−12)/(2x^2)÷(x^2+x−6)/2x^3$

First write the given term in the correct form by multiplying with reciprocal of denominator.

Given term =  $(x^2−x−12)*2x^3/(2x^2)*(x^2+x-6)$

Now we find that numerator = $(x^2−x−12)*2x^3$

= [tex]2x^3(x-4)(x+3)[tex]

Similarly denominator = [tex]2x^3/(2x^2)*(x^2+x-6)[tex]

=[tex](2x^3(x+3)(x-2)[tex]

Common factor in both numerator and denominator = [tex][2x^2(x+3)(xtex]

So cancel this to get

[tex]x(x-4)/(x-2)[tex]