Question

How do you combine `(4x+y)/(2x+3y) - (2x-2y)/(2x+3y)`?

Answer 1

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

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

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

`=1`

Answer 2

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

`={1/(2x+3y)*(4x+y)}-{1/(2x+3y)*(2x-2y)}`

Taki ng `1/((2x+3y)` common,

`=(1/(2x+3y)*[+(4x+y)-(2x-2y)]`

`=1/(2x+2y)*(4x+y -2x + 2y)`

`=1/(2x+2y)*(4x - 2x + y +2y)`

`=1/(2x+2y)*(2x+3y)`
Cancelling common factors from numerator and denominator,
`=1`