<s>[INST] Solve $\frac{5}{x+3}+\frac{2}{2x+6}=4$ I want to solve $\frac{5}{x+3}+\frac{2}{2x+6}=4$ for $x$
I try this;
$5(2x+6)+2(x+3)=4(x+3)(2x+6)$
$12x+36 = 4(2x^2+12x+18)$
$8x^2+36x+36=0$
Where I would then go to the formula, however the answer says -1.5, what am I doing wrong.
 [/INST] You could solve it this way:
The second fraction, $\frac {2}{2x+6}$ can be simplified into $\frac 1{x+3}$. Thus,
$$\frac 5{x+3}+\frac 2{2x+6}=4\implies\frac 6{x+3}=4\tag1$$
And cross multiplying, we get $4(x+3)=6\implies x=x=-\frac 32$

As to where you went wrong, nothing has gone wrong yet. Use the quadratic formula and see what you get!

 Hint: You will get two solutions. One of them doesn't work (i.e it's extraneous).

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