The solution of x+a/x-2a = x+3a/x-4a is ​

Question

The solution of \(\frac{x + a}{x - 2a} = \frac{x + 3a}{x - 4a}\) is

(a) x = a

(b) x = –a/2

(c) x = a/2

(d) x = – a

Answer 1

Correct option is (c) x = a/2

\(\frac{x + a}{x - 2a} = \frac{x + 3a}{x - 4a}\)

(x + a) (x − 4a) = (x + 3a)(x − 2a)

x² + ax − 4ax − 4a² = x² + 3ax − 2ax − 6a²

−3ax − 4a² = ax − 6a²

2a² = 4ax

x = \(\frac{2a^2}{4a} \) = \(\frac a2\)