Answer:
a) x = 1 is a solution
c) x = -1 is also solution
Step-by-step explanation:
Explanation:-
Given rational equation
[tex]\frac{4}{x+6} + \frac{1}{x^{2} } = \frac{x+10}{x^{2} (x+6)}[/tex]
Now L.C.M and simplification, we get
[tex]\frac{4x^{2} +X+6}{x^{2} (x+6)} = \frac{x+10}{x^{2}(x+6) }[/tex]
Now cancellation x²(x+6) on both sides, we get
4x²+x+6 = x +10
On simplification , we get
4x² +x+6 -x-10=0
4x²-4 =0
4(x²-1) =0
x²-1 =0
Apply Formula a²-b² = (a-b)(a + b)
(x-1)(x+1) =0
x =1 and x=-1
Hence x =1 and x =-1 is a solution of given rational function
