Question

Question #3f27d

Answer 1

Solution given with a bit expanded explanations

Explanation:

Given:`" "50/(x+2)=2x+10`

To remove the `x` from the denominator multiply both sides by `(x+2)`

`50xx(x+2)/(x+2)=(x+2)(2x+10)`

But `(x+2)/(x+2)=1 and 50xx1 =50`

`50=color(blue)((x+2))color(green)((2x+10))`

Multiply everything in the right hand brackets (green) by everything in the left hand brackets (blue) giving:

`50=color(blue)((x))color(green)((2x+10)" "+" "color(blue)(2)color(green)((2x+10)))`

`50=" "2x^2+10x" "+" "4x+20`

`50=2x^2+14x+20`

Everything is even so reduce the number values by dividing both sides by 2. The equation is still true; what you do to one side you do to the other.

`25=x^2+7x+10`

Subtract 25 from both sides

`0=-x^2+7x-15`

We now have a quadratic and you solve as per the method used by Rithvik