solve the following rational equation.\n$\frac{6}{x + 4}=x + 5$\n$x = ?, $

Explanation:

Step1: Cross - multiply

$6=(x + 5)(x + 4)$

Step2: Expand the right - hand side

$6=x^{2}+4x+5x + 20$ $6=x^{2}+9x + 20$

Step3: Rearrange to form a quadratic equation

$x^{2}+9x+20 - 6=0$ $x^{2}+9x + 14=0$

Step4: Factor the quadratic equation

$(x + 2)(x+7)=0$

Step5: Solve for x

$x+2 = 0$ gives $x=-2$ $x + 7=0$ gives $x=-7$

Answer:

$x=-2,-7$