Simplify the question

Question

3x+6/x+2 divided by x^2+2x-3/6x^2+6x-12

Answer 1

Hi Zack, the way to approach this type of problem is to try to reduce and / or factor it in pieces.

 

Step 1:

 

3x + 6 / x + 2

 

Factor out the 3 in the numerator gives:

 

3 * (x + 2) / (x + 2)

 

The (x + 2) cancels in the numerator and denominator leaving:

 

3/1

 

Step 2:

 

x² +2x - 3 / 6x² + 6x - 12

 

Factor the numerator:

 

x² + 2x - 3 = (x + 3) * (x - 1)

 

Factor the denominator:

 

6x² + 6x - 12

 

Factor out the 6 leaving giving:

 

6 * (x² + x - 2)

 

Factor x² + x - 2 = (x + 2) * (x - 1)

 

Combine results of the factoring:

 

(x + 3) * (x - 1) / (6 * (x + 2) * (x - 1))

 

the (x - 1) cancels in the numerator and denominator leaving:

 

x + 3 / (6 * (x + 2))

 

Step 3:

 

This is what is left after the canceling:

 

Numerator / Denominator

(3 / 1)      / ( (x + 3) / (6 * (x + 2) )

 

To solve: invert the denominator and multiply:

 

(3 / 1) * (6 * (x + 2) / (x + 3))

 

Combine numerators and denominators:

 

(3 * 6 * (x + 2) ) / (x + 3)

 

(18 * (x + 2)) / (x + 3)

 

Questions?