Question #3f27d

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Answer 1 · 2017-03-20T19:26:29

Solution given with a bit expanded explanations

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