Question

What is the quotient of the rational expressions shown below? Make sure
your answer is in reduced form.
x2 + 5x +6/x-6/x^2-9/2x-12

Answer 1

Picture of the right answers

Answer 2

Hence, the quotient of the rational expression given below is x-3.

How to solve?

To solve the division we will use basic properties of rational numbers here.

The first step is to factor numerator/denominator if possible.

To divide the expressions follow the following steps

1.leave the first fraction as it is

2. Convert division to multiplication

3.Turn the second fraction upside down

($x^{2}$+5x+6)/x-6 / ($x^{2}$-9)/2x-12

=($x^{2}$+5x+6)(2(x-6))/($x^{2}$-9)(x-6)

=2($x^{2}$+5x+6)/$x^{2}$-9

By splitting the quadratic equation into factors we get,

$x^{2}$+5x+6=(x+2)(x+3)

and using the formula $a^{2}$-$b^{2}$=(a-b)(a+b) we get $x^{2}$-9=(x-3)(x+3)

=2(x+3)(x+2)/(x+3)(x-3)

=2(x+2)/(x-3)

hence, the quotient of the given ration expression is x-3.

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