Question

What is the quotient of the rational expressions shown below? Make sure your answer is in reduced form.

x^2 +5x+4/x-1 / x^2 - 16/3x-3

Answer 1

hello: here is a solution 

Answer 2

Answer: The quotient of the rational expression is 3.

Explanation:

since we have given that

`((x^2+5x+4)/(x-1))/((x^2-16)/(3x-3))`

We need to solve for the quotient ;

We will change it in reduced form:

`((x^2+5x+4)/(x-1))/((x^2-16)/(3x-3))\\\\=((x^2+5x+4)* (3x-3))/((x^2-16)* (x-1))`

First we solve the quadratic equation by using "Split the middle term":

`x^2+5x+4\\\\=x^2+4x+x+4\\\\=x(x+4)+1(x+4)\\\\=(x+4)(x+1)`

Now, put the factorised form in the above expression:

`((x^2+5x+4)* (3x-3))/((x^2-16)* (x-1))\\\\=((x+4)(x+1)* 3(x-1))/((x+4)(x-4)(x-1))\\\\=(3(x+1))/(x-4)\\\\=(3x+3)/(x-4)\\\\=3+(15)/(x-4)`

Hence, the quotient of the rational expression is 3.