Answer
$x=-4$ and $x=-\dfrac{7}{3}$
Work Step by Step
$\dfrac{x}{2x+7}-\dfrac{x+1}{x+3}=1$
Evaluate the substraction on the left:
$\dfrac{x(x+3)-(x+1)(2x+7)}{(2x+7)(x+3)}=1$
$\dfrac{x^{2}+3x-[2x^{2}+9x+7]}{2x^{2}+13x+21}=1$
$\dfrac{x^{2}+3x-2x^{2}-9x-7}{2x^{2}+13x+21}=1$
$\dfrac{-x^{2}-6x-7}{2x^{2}+13x+21}=1$
Take the denominator to multiply the right side of the equation. We get:
$-x^{2}-6x-7=2x^{2}+13x+21$
Take all terms to the right side of the equation:
$2x^{2}+13x+21+x^{2}+6x+7=0$
Simplify:
$3x^{2}+19x+28=0$
Solve by factoring:
$(3x+7)(x+4)=0$
We get two solutions, which are:
$x=-4$ and $x=-\dfrac{7}{3}$
