Answer:
3rd option
Step-by-step explanation:
[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] ( factorise numerator and denominator )
3x² - 3 ← factor out 3 from each term
= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
x² - 1
= x² - 1²
= (x - 1)(x + 1) , then
3x² - 3 = 3²(x - 1)(x + 1) ← in factored form
--------------------------------
x² - 5x + 4
consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)
the factors are - 1 and - 4 , since
- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then
x² - 5x + 4 = (x - 1)(x - 4)
then
[tex]\frac{3x^2-3}{x^2-5x+4}[/tex] = [tex]\frac{3(x-1)(x+1)}{(x-1)(x-4)}[/tex] ← in factored form