Question

find the roots of the equation 1/x+3 + 1/ 2x-1 =
11/7x-9​

Answer 1

Answer:

Step-by-step explanation:

We have

1(x+3)+1(2x−1)=11(7x+9)

⇒ (2x−1)+(x+3)(x+3)(2x−1)=11(7x+9)⇒(3x+2)2x2+5x−3=11(7x+9)

⇒ (3x+2)(7x+9)=11(2x2+5x−3) [by cross multiplication]

⇒ 21x2+41x+18=22x2+55x−33

⇒ x2+14x−51=0⇒x2+17x−3x−51=0

⇒ x(x+17)−3(x+17)=0⇒(x+17)(x−3)=0

⇒ x+17=0 or x−3=0

⇒ x=−17 or x=3.

Hence, -17 and 3 are the roots of the given equation.