Answer:
x = 4 , x = 2.4
Explanation:
+
= 5
multiply through by (x - 2)(x - 3)
4(x - 3) + 3(x - 2) = 5(x - 2)(x - 3)
4x - 12 + 3x - 6 = 5(x² - 5x + 6)
7x - 18 = 5x² - 25x + 30 ( subtract 7x - 18 from both sides )
0 = 5x² - 32x + 48
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 5 × 48 = 240 and sum = - 32
the factors are - 20 and - 12
use these factors to split the x- term
0 = 5x² - 20x - 12x + 48 ( factor the first/second and third/fourth terms )
0 = 5x(x - 4) - 12(x - 4) ← factor out (x - 4) from each term
0 = (x - 4)(5x - 12)
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
5x - 12 = 0 ⇒ 5x = 12 ⇒ x = 2.4