How do you simplify #((3x-2)/(x^2-4))/((5x+1)/(x^2+x-6))#?

1 Answer

Answer:

#((3x-2)(x+3))/((x+2)(5x+1))=(3x^2+7x-6)/(5x^2+11x+2)#

Explanation:

Let's first rewrite the division of fractions to a multiplication of fractions:

#((3x-2)/(x^2-4))/((5x+1)/(x^2+x-6))#

#((3x-2)/(x^2-4))((x^2+x-6)/(5x+1))#

And now let's factor what we can:

#((3x-2)/((x-2)(x+2)))(((x+3)(x-2))/(5x+1))#

The #x-2# terms cancel, so we get:

#((3x-2)(x+3))/((x+2)(5x+1))#

We can also write this as:

#(3x^2+7x-6)/(5x^2+11x+2)#