Question

1 upon x-3 -1 upon x-5= 1 upon 6​

Answer 1

Answer:

x = -9 or x = 7

Kindly refer to the attachment for step by step solution.

Answer 2

Given :

$\huge\frac{1}{x - 3}$ - $\huge\frac{1}{x + 5}$ = $\huge\frac{1}{6}$ .... where x is neither equal to 3 nor -5

To find :

Roots of the given equation; two values of x which satisfies the given equation

Solution :

$\huge\frac{1}{x - 3}$ - $\huge\frac{1}{x + 5}$ = $\huge\frac{1}{6}$

On taking L.C.M,

》$\huge\frac{x + 5 - x + 3}{(x - 3)(x + 5)}$ = $\huge\frac{1}{6}$

》$\huge\frac{8}{x^2 + 2x - 15}$ = $\huge\frac{1}{6}$

On cross multiplying,

》x² + 2x - 15 = 48

》x² + 2x - 15 - 48 = 0

》x² + 2x - 63 = 0

》x² + 9x - 7x - 63 = 0

》x(x + 9) - 7(x + 9) = 0

》(x + 9)(x - 7) = 0

•°• x + 9 = 0

x = -9

OR

•°• x - 7 = 0

x = 7

Required roots = -9 and 7