Question

How to simplify the following? `2/(x(2x-3y))-3/(2x(x+4y))`

Answer 1

`(25y-2x)/(2x(2x-3y)(x+4y)`

Explanation:

`"before we can subtract the fractions they must have a "`
`color(blue)"common denominator"`

`"to achieve this "`

`• " multiply the numerator/denominator of "`

`2/(x(2x-3y))" by "2(x+4y)=2x+8y`

`• " multiply the numerator/denominator of "`

`3/(2x(x+4y))" by "(2x-3y)`

`rArr(2(2x+8y))/(2x(2x-3y)(x+4y))-(3(2x-3y))/(2x(2x-3y)(x+4y))`

`"we now have a common denominator and can subtract the"`
`"numerators leaving the denominator"`

`=(4x+16y-6x+9y)/(2x(2x-3y)(x+4y))`

`=(25y-2x)/(2x(2x-3y)(x+4y))`

Answer 2

`=(-2x+25y)/(2x(2x-3y)(x+4y))`

Explanation:

You are subtracting two fractions so you need the `LCD`

This will be `2x(2x-3y)(x+4y)`

Multiply each fraction by whatever factors are missing to form the common denominator.

`2/(x(2x-3y)) xx (2(x+4y))/(2(x+4y)) -3/(2x(x+4y))xx((2x-3y))/((2x-3y))`

`= (4(x+4y) -3(2x-3y))/(2x(2x-3y)(x+4y))`

`=(4x+16y-6x+9y)/(2x(2x-3y)(x+4y))`

`=(-2x+25y)/(2x(2x-3y)(x+4y))`