Question

Factoriz 4/x+2-1/x+3=4/2x+1

Answer 1

Answer:

answer is (2x-1)(x-10)

Step-by-step explanation:

given

4/X+2-1/X+3=4/2x+1

when we take lcm

4(x-3)-(X+2)/(X+2(x-3). = 4/2x+1

4x-12-x-2 / X square - 3x +2x -6 =4/2x+1

3x-14 /X square -x-6 = 4/2x+1

(2x+1)(3x-14) = 4(X square - x-6

6x square -28x +3x-14 = 4 X square-4x -24

6xsquare -4x square-25x+4x-14+24=0

2x square -21x+10 =0

2x square-x-20x square +10=0

X(2x-1) -10(2x-1) =0

(x-10)(2x-1) = 0

x =10 and 1/2

Answer 2

4/x+2 - 1/x+3 = 4/2x+1 ⇒ [4(x + 3) - 1(x + 2)] / [(x + 2)(x + 3)] = 4/(2x + 1) ⇒ [4x + 12 - x - 2] / [x2 + 5x + 6] = 4/(2x + 1) ⇒ [3x + 10] / [x2 + 5x + 6] = 4/(2x + 1) ⇒ 4x2 + 20x + 24 = 6x2 + 23x + 10 ⇒ 2x2 + 3x - 14 = 0 ⇒ (x - 2)(2x + 7) = 0 ⇒ x = 2 or - 7/2