Question

Solve the following?

Answer 1

Note: The correct answer is here.

Explanation is wrong, I might come back and fix it later.

Explanation:

Common denominator shall be `(x+2)(x+5)`, so
`(2x(\color(red)(x+5)))/((x+2)(\color(red)(x+5)))=(3x(\color(blue)(x+2)))/((x+5)(\color(blue)(x+2)))-(1(\color(red)(x+5))(\color(blue)(x+2)))/((\color(red)(x+5))(\color(blue)(x+2))`

Now you have the same denominator overall. You can remove it to make your work easier.
`2x(x+5)=3x(x+2)-1(x+5)(x+2)`

Apply distributive property,
`2x(x)+2x(5)=3x(x)+3x(2)-\color(olive)((x+5)(x+2))`

We will do the green part later. First we simplify what I have distributed...
`2x^2+10x=3x^2+6x-\color(olive)((x+5)(x+2))`
`-x^2+4x=\color(olive)((x+5)(x+2))`

Now we will FOIL the green part.
`color(olive)((x+5)(x+2))=x(x)+x(2)+5(x)+5(2)`
`=x^2+2x+5x+10=x^2+7x+10`

And so...
`\therefore-x^2+4x=\color(olive)(x^2+7x+10)`

Moving everything to right side,
`0=2x^2+3x+10`

Now let's do quadratic formula, see here

Looks like we have an imaginary answer...
`-3/4\pmi\sqrt(71)/4`