Question

$\frac{9}{x-8} + \frac{15}{x^2-64} = \frac{10}{x+8} ; x\neq 8,-8$

Answer 1

Answer:

The given equations are:  9/x - 4/y  = 8 ……..(i)  13/x + 7/y = 101 ……..(ii)  Putting 1/x = u and 1/y = v, we get:  9u - 4v = 8 …….(iii)  13u + 7v = 101 ……(iv)  On multiplying (iii) by 7 and (iv) by 4, we get:  63u - 28v = 56 ……..(v)  52u + 28v = 404 ……..(vi)  On adding (v) from (vi), we get:  115u = 460  ⇒ u = 4  ⇒ 1/ x = 4  ⇒ x = 1/4  On substituting x = 1/ 4 in (i), we get:  9/ 1/ 4 - 4/ y = 8  ⇒36 - 4/ y = 8  ⇒ 4/ y = (36 – 8) = 28  y = 4/ 28 = 1/7  Hence, the required solution is x = 1/4 and y = 1/ 7.