Question

Solve using factorisation method

Pls help

Rd Sharma class 10 ex :-4.3 no :- 45

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

Answer 1

Answer:

x = 0, x = a + b

Step-by-step explanation:

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

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

=> (x - a)²(x - b)²/(x² - ax - bx + ab) = a² + b²/ab

=> (x² - 2ax + a² + x² - 2bx + b²)/x² - (a + b)x + ab = a² + b²/ab

=> 2abx² - 2abx(a + b) + ab(a² + b² = (a² + b²)x² - (a² + b²)(a+b)x + ab(a²+b²)

=> (a²+b²+2ab)x² - (a+b)(a²+b²-2ab)x=0

=> (a-b)²x² - (a+b)(a-b)²x = 0

=> (a-b)²(x-(a+b))=0

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

=> x = 0, x = a+b.

#Hope my answer helped you.