(Q21)Find the roots of the following equations

(ii)
1
x+4
-
1
x-7
=
11
30
,x ≠-4,7

Answer:

Given:
1
x+4
-
1
x-7
=
11
30

(x-7)-(x+4)
(x+4)(x-7)
=
11
30

x-7-x-4
(x+4)(x-7)
=
11
30

-
x2-7x+4x-28
=
11
30

-
x2-3x-28
=
1
30

x2 - 3x - 28 = -30

x2 - 3x - 28 + 30 = 0

x2 - 3x + 2 = 0

x2-x - x + 2 = 0

x(x - )- 1(x - )=0

(x - )(x - 1) = 0

x - = 0 (or) x - 1 = 0

x = (or) x = 1

x = (or) 1.