Question

solve the equation please ...​

Answer 1

Answer:

x = (a + b) (or) x = (a + b)/2

Step-by-step explanation:

Equation is (a/x - b) + (b/x - a) = 2

Take the LCM of denominators in the left hand side of the given equation.

=> a(x - a) + b(x - b)/(x - b)(x - a) = 2

=> a(x - a) + b(x - b) = 2(x - b)(x - a)

=> ax - a^2 + bx - b^2 = 2[x^2 - ax - bx + ab]

=> ax - a^2 + bx - b^2 = 2x^2 - 2ax - 2bx + 2ab

=> 2x^2 - 2ax - 2bx + 2ab - ax + a^2 - bx + b^2 = 0

=> 2x^2 - 3ax - 3bx + a^2 + b^2 + 2ab = 0

=> 2x^2 - 3x(a + b) + (a^2 + b^2 + 2ab) = 0

=> 2x^2 - 3x(a + b) + (a + b)^2 = 0

=> 2x^2 - 2x(a + b) - x(a + b) + (a + b)^2 = 0

Take 2x common.

=> 2x[x - (a + b))] - (a + b)[x - (a + b)] = 0

=> (x - (a + b))(2x - (a + b)) = 0

=> x = a + b (or) x = (a + b)/2

Hence, the values are x = (a + b) (or) x = (a + b)/2

#Hope my answer helped you!

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment (1) & (2)