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:

`(2)/(x+2)+(1)/(5)=(6)/(x+5)`

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

`(10+(x+2))/(5(x+2))=(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`