Question

How do you simplify and find the restrictions for `((3x)/y -x/1) / ((2y)/1 - y/x)`?

Answer 1

`= (x^2(3-y))/(y^2(2x-1))`

`x !=0 and y!=0`

Explanation:

`((3x)/y -x/1) / ((2y)/1 - y/x)" " x !=0 and y!=0`

Before we start with any simplifying we can see that the denominators at the top and bottom have an `x` and a `y`
Therefore, they may not be `0`
We might find further restrictions later.

Write the complex fraction as a division of two fractions:

`((3x)/y -x/1) div ((2y)/1 - y/x)` find LCD and subtract as usual,.

`= ((3x-xy))/y div ((2xy-y))/x" "larr` factorise the numerators:

`= (x(3-y))/y div (y(2x-1))/x" "larr` multiply by the reciprocal

`=(x(3-y))/y xx x/(y(2x-1))`

`= (x^2(3-y))/(y^2(2x-1))`

The original restrictions are confirmed.