Question

Solve for x: 2 over quantity x plus 2 plus 1 over 5 equals 6 over quantity x plus 5. x = 0 x = −13 x = 13 x = 0 and x = 13

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have the following expression given in the problem above:

$\frac{2}{x+2}+\frac{1}{5}=\frac{6}{x+5}$

2. You need to sum the fractions located on the left member, as following:

$\frac{10+(x+2)}{5(x+2)}=\frac{6}{x+5}$

$x=(12+x)(x+5)=6(5x+10)$

3. Simplify it and you will obtain a quadratic equation. Solve it by factor out $x$:

$x^{2} -13x=0\\ x(x-13)=0\\ x=0; x=13$

Therefore, the answer is: $x=0; x=13$