Question

How do you simplify `((3x-1) / (x^2+5x)) - ((2x-1) / (x^2-25))`?

Answer 1

`(x^2-15x+5)/(x(x+5)(x-5))`

Explanation:

`(3x-1)/(x^2+5x)-(2x-1)/(x^2-25)`

Factorise your denominator
=`(3x-1)/(x(x+5))-(2x-1)/((x-5)(x+5))`

Now you want to make your denominator the same
=`((3x-1)(x-5)-(2x-1)(x))/(x(x+5)(x-5))`

Expand your brackets
=`(3x^2-16x+5-2x^2+x)/(x(x+5)(x-5))`

Simplify
=`(x^2-15x+5)/(x(x+5)(x-5))`

Answer 2

`(x^2-15x+5)/((x(x+5)(x-5))`

Explanation:

Writing
`(3x-1)/(x(x+5))-(2x-1)/((x-5)(x+5))`
as

`((3x-1)(x-5))/(x(x+5)(x-5))-(x(2x-1))/((x(x-5)(x+5))`
this is equal to

`(3x^2-x-15x+5-(2x^2-x))/(x(x-5)(x+5))`
collecting likewise terms

`(x^2-15x+5)/(x(x+5)(x-5))`