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:

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

`((2)(5)+(x+2))/(5(x+2)) =(6)/((x+5))\\((x+12))/((5x+10))=(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`