Question

Given that p=x^2-y^2/x^2+xy

I. Express p in the simplest form
ii. Find the value of p if x=-4 and y=-6

Answer 1

p = -
`(1)/(2)`

Explanation:

Given

p =
`(x^2-y^2)/(x^2+xy)` ( factorise numerator and denominator )

x² - y² ← is a difference of squares and factors as (x - y)(x + y)

x² + xy ← factor out x from each term

= x(x + y) , thus

p =
`((x-y)(x+y))/(x(x+y))` ← cancel (x + y) on numerator/ denominator

=
`(x-y)/(x)` ← substitute x = - 4, y = - 6

=
`(-4-(-6))/(-4)`

=
`(-4+6)/(-4)`

=
`(2)/(-4)` = -
`(1)/(2)`