Question

What is the simplified form of x^2 - 25 / x^2 - 3x - 10

Answer 1

`{(x^2-25)/(x^2-3x-10)=(x^2-25)/(x^2+2x-5x-10)=((x+5)(x-5))/(x(x+2)-5(x+2))=((x+5)(x-5))/((x+2)(x-5))=(x+5)/(x+2)}`

domain

`x\\e -2\ , \ x\\e 5\\\\ D: \ x \in \math R \backslash \{-2, 5\}`

Answer 2

(x² - 25) / (x2 - 3x - 10)

1) Expand the 1st factor: (x² - 25) = (x-5)(x+5)

2) factorize the 2nd: (x2 - 3x - 10), it's a quadratic equation with 5 & -2 as roots.
Then (x2 - 3x - 10) = (x-5)(x+2)

3) replace the latter in (x² - 25) / (x2 - 3x - 10)

===>(x-5)(x+5) / (x-5)(x+2)==>after simplifying Numerator & Denominator we

will get :(x+5) / (x+2)