Solve the equation $5 + 2x = \dfrac{20}{1 + x}$. Answer x = ... or ...

1. State the restriction and clear the denominator.

Since $1+x\neq 0$, $x\neq -1$.
$5+2x=\frac{20}{1+x}$
Multiply both sides by $1+x$:
$(5+2x)(1+x)=20$

2. Expand and rearrange into standard quadratic form.

$(5+2x)(1+x)=20$
$5+5x+2x+2x^2=20$
$2x^2+7x+5=20$
$2x^2+7x-15=0$

3. Factorise and solve the quadratic equation.

$2x^2+7x-15=0$
$(2x-3)(x+5)=0$
So,
$2x-3=0 \quad \text{or} \quad x+5=0$
$x=\frac{3}{2} \quad \text{or} \quad x=-5$