Question

solve for X 300/x-5 -300/X=5​

Answer 1

Answer:

-15, 20

Step-by-step explanation:

300/x-5 -300/X=5

(300x-300x+1500)/x(x-5)=5

1500/(x^2-5x)=5

1500/5=(x^2-5x)

(x^2-5x)=300

x^2-5x-300=0

x^2-20x+15x-300=0

x(x-20)+15(x-20)=0

(x+15)(x-20)=0

if, x+15=0→ x= -15

or, (x-20)=0→ x= 20

Answer 2

$\sf\huge {\underline{\underline{{Solution}}}}$

$\sf \longmapsto \dfrac{300}{x - 5} - \dfrac{300}{x} = 5$

Taking LCM of x-5 and x

$\sf \longmapsto \dfrac{300(x) - 300(x - 5)}{x(x - 5)} = 5$

$\sf \longmapsto \dfrac{300x - 300x + 1500}{ {x}^{2} - 5x } = 5$

$\sf \longmapsto \dfrac{1500}{ {x}^{2} - 5x} = 5$

Now, cross multiply to both sides

$\sf \longmapsto1500 = 5( {x}^{2} - 5x)$

$\sf \longmapsto \dfrac{1500}{5} = {x}^{2} - 5x$

$\sf \longmapsto300 = {x}^{2} - 5x$

$\sf \longmapsto {x}^{2} - 5x - 300$

Now, it is in the form of a quadratic equation so factorise it .

$\sf \longmapsto {x}^{2} - 20x + 15x - 300 = 0$

$\sf \longmapsto \: x(x - 20) + 15(x - 20) = 0$

$\sf \longmapsto(x + 15)(x - 20) = 0$

$\sf x - 20 = 0$

$\sf \bold{x = 20}$

$\sf x + 15 = 0$

$\sf \bold{ x = - 15}$

Check

=> 300/x-5-300/x=5

Taking LHS

at x = 20

=> 300/20-5-300/20

=> 300/15-300/20

=> 20-15

= 5