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:

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

2. You need to find the least common denominator on the rigth member of the equation and then, you must sum both fractions:

$\frac{(2)(5)+(x+2)}{5(x+2)} =\frac{6}{(x+5)}\\\frac{(x+12)}{(5x+10)}=\frac{6}{(x+5)}$

3. Now, solve for $x$, as following:

$(x+12)(x+5)=6(5x+10)\\ x^{2} -13x=0$

4. Factor out the $x$:

$x(x-13)=0\\ x=0; x=13$

The answer is: $x=0\\ x=13$