Question

Simplest Form? How to do this?

Answer 1

`(x-3)/2`

Explanation:

`"multiply numerator/denominator by x to eliminate"`
`"the fractions"`

`rArr(x-9/x)/(2+6/x)xx x/x`

`=(x^2-9/cancel(x)xxcancel(x))/(2x+6/cancel(x)xxcancel(x))`

`=(x^2-9)/(2x+6)`

`"factorise numerator/denominator"`

`x^2-9" is a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"here "a=x" and "b=3`

`rArrx^2-9=(x-3)(x+3)`

`2x+6=2(x+3)larrcolor(blue)"common factor of 2"`

`rArr(x^2-9)/(2x+6)`

`=((x-3)cancel((x+3)))/(2cancel((x+3)))larrcolor(blue)"cancel common factors"`

`=(x-3)/2larr" in form "(A(x+B))/C`

`"with "A=1,B=-3" and "C=2`