Question

find the sum of the roots of the equation
1/x-3-1/x-5=1/6​

Answer 1

Answer:

Given equation is:  

x−3

1

​

−  

x+5

1

​

=  

6

1

​

 

⇒  

(x−3)(x+5)

x+5−(x−3)

​

=  

6

1

​

 

⇒  

x  

2

+2x−15

x+5−x−3

​

=  

6

1

​

 

⇒  

x  

2

+2x−15

8

​

=  

6

1

​

 

⇒48=x  

2

+2x−15

⇒x  

2

+2x−63=0

⇒x  

2

+9x−7x−63=0

⇒x(x+9)−7(x+9)=0

⇒(x+9)(x−7)=0

⇒x+9=0 or x−7=0

⇒x=−9 and x=7

Hence, x=−9,7 are the required solutions.

Step-by-step explanation:

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