Question

Solve the following quadratic equations by factorization: 

`100/x-100/(x+5)=1` 

 

Answer 1

`100/x-100/(x+5)=1`   

⟹`( 100(x+5)-100x)/(x(x+5))=1` 

⟹ `500/(x^2+5x)=1` 

⟹` x^2 + 5x = 500`
⟹ `x^2 + 5x – 500 = 0`
⟹ `x^2 + 25x – 20(x + 25) = 0`
⟹ `x(x + 25) (x – 20) = 0`
If `x + 25 = 0  Or  x – 20 = 0`
Then` x = − 25  Or  x = 20 `