# Question #3f27d

Mar 20, 2017

Solution given with a bit expanded explanations

#### Explanation:

Given:$\text{ } \frac{50}{x + 2} = 2 x + 10$

To remove the $x$ from the denominator multiply both sides by $\left(x + 2\right)$

$50 \times \frac{x + 2}{x + 2} = \left(x + 2\right) \left(2 x + 10\right)$

But $\frac{x + 2}{x + 2} = 1 \mathmr{and} 50 \times 1 = 50$

$50 = \textcolor{b l u e}{\left(x + 2\right)} \textcolor{g r e e n}{\left(2 x + 10\right)}$

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

$50 = \textcolor{b l u e}{\left(x\right)} \textcolor{g r e e n}{\left(2 x + 10\right) \text{ "+" } \textcolor{b l u e}{2} \textcolor{g r e e n}{\left(2 x + 10\right)}}$

$50 = \text{ "2x^2+10x" "+" } 4 x + 20$

$50 = 2 {x}^{2} + 14 x + 20$

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.

$25 = {x}^{2} + 7 x + 10$

Subtract 25 from both sides

$0 = - {x}^{2} + 7 x - 15$

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