Question

This is the equation:


`(16-c^2)/(c^2+c-20)`
and these are my steps:

`((c+4)(c-4))/((c-4)(c+5)) \\=(c+4)/(c+5)`
but the calculator answer is:

`-(c+4)/(c+5)`
why did it turn negative?

Answer 1

see explanation

Explanation:

you have factored c² - 16 instead of 16 - c²

given

`(16-c^2)/(c^2+c-20)` ← factor out - 1 on the numerator , thus obtaining c² - 16

=
`(-(c^2-16))/(c^2+c-20)`

factor numerator as a difference of squares and the denominator by quadratic factorising

=
`(-(c+4)(c-4))/((c-4)(c+5))` ← cancel the common factor (c - 4 ) on numerator/denominator

=
`(-(c+4))/((c+5))`

= -
`(c+4)/(c+5)`