Question

1/x-3+2/x-2=8/x
solve this quadratic equation by factorization​

Answer 1

Answer:

x−3

1

+

x−2

2

=

x

8

⇒

(x−3)(x−2)

x−2+2(x−3)

=

x

8

⇒

x

2

−2x−3x+6

x−2+2x−6

=

x

8

⇒

x

2

−5x+6

x+2x−8

=

x

8

⇒ x

2

+2x

2

−8x=8x

2

−40x+48

⇒ 3x

2

−8x=8x

2

−40x+48

⇒ 5x

2

−32x+48=0

⇒ 5x

2

−20x−12x+48=0

⇒ 5x(x−4)−12(x−4)=0

⇒ (x−4)(5x−12)=0

⇒ x−4=0 and 5x−12=0

∴ x=4 and x=

5

12

Answer 2

Answer:

Given that 1/x-3 + 2/x-2 = 8/x.

Taking LCM.

{x-2+ 2(x-3)}/(x-3)(x-2)= 8/x.

x-2 + 2x-6/x2– 2x- 3x -6 = 8/x.

3x – 8/x2 – 5x – 6 = 8/x.

Next we have to cross multiply

⇒ x(3x – 8) = 8(x – 3)(x – 2)

⇒ 3×2 – 8x = 8(x2 – 5x + 6)

⇒ 8×2 – 40x + 48 – (3x2 – 8x) = 0

⇒ 5x2 – 32x + 48 = 0

⇒ 5x2 – 20x – 12x + 48 = 0

⇒ 5x(x – 4) – 12(x – 4) = 0

⇒ (x – 4)(5x – 12) = 0

Now, either x – 4 = 0

⇒ x = 4 Or, 5x – 12 = 0

⇒ x = 5/12