Question

please answer this question as soon as possible ​

Answer 1

Answer:

2(3x-5)÷(x+2) -5(x+2) ÷(3x-5) =3

(6x-10) ÷(x+2) -(5x+10) ÷(3x-5) =3

[(6x-10) (3x-5) -(5x+10) (x+2) ]÷(3x²+x-2) =3

(18x²-60x+50)-(5x²+20x+20) = 3(3x²+x-10)

18x²-60x+50-5x²-20x-20=9x²+3x-30

On solving, we get

4x²-83x+60=0

4x²-(80+3)x+60=0

4x²-80x-3x+60=0

4x(x-20)-3(x-20)=0

(x-20)(4x-3)=0

So, x-20=0

x=20

4x-3=0

x=3÷4

So, x is equal to 20 and 3÷4

Answer 2

Question: Solve the equation 2(3x-5)/(x+2) - 5(x+2)/(3x-5) = 3, where x ≠ -2 an x≠5/3.

Answer:

3/4 or 20

Step-by-step explanation:

Let (3x - 5)/(x + 2) = t, so (x + 2)/(3x - 5) = 1/t

Therefore,

=> 2t - 5/t = 3

=> 2t² - 5 = 3t

=> 2t² - 3t - 5 = 0

=> 2t² - (5 - 2)t - 5 = 0

=> 2t² + 2t - 5t - 5 = 0

=> 2t(t + 1) - 5(t + 1) = 0

=> (t + 1)(2t - 5) = 0

=> t = -1 or t = 5/2

Therefore,

(3x - 5)/(x + 2) = -1 or (3x - 5)/(x + 2) = 5/2

3x - 5 = -x-2 or 6x - 10 = 5x + 10

4x = 3 or x = 20

x = 3/4 or x = 20