Question

60/8+X + 60/8-X = 16

Answer 1

Answer:

x = -2 or x = 2

Step-by-step explanation:

$Domain:\\8+x\neq0\ \wedge\ 8-x\neq0\\\boxed{D:x\neq-8\ \wedge\ x\neq8}\\\\\dfrac{60}{8+x}+\dfrac{60}{8-x}=16\\\\\dfrac{60(8-x)}{(8+x)(8-x)}+\dfrac{60(8+x)}{(8+x)(8-x)}=16\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{60(8-x)+60(8+x)}{8^2-x^2}=16\qquad\text{use the distributive property}\\\\\dfrac{(60)(8)+(60)(-x)+(60)(8)+(60)(x)}{64-x^2}=16\\\\\dfrac{480-60x+480+60x}{64-x^2}=16\qquad\text{combine like terms}\\\\\dfrac{(480+480)+(-60x+60x)}{64-x^2}=16\\\\\dfrac{960}{64-x^2}=16$

$\dfrac{960}{64-x^2}=\dfrac{16}{1}\qquad\text{cross multiply}\\\\16(64-x^2)=(960)(1)\qquad\text{use the distributive property}\\\\(16)(64)+(16)(-x^2)=960\\\\1024-16x^2=960\qquad\text{subtract 1024 from both sides}\\\\1024-1024-16x^2=960-1024\\\\-16x^2=-64\qquad\text{divide both sides by (-16)}\\\\\dfrac{-16x^2}{-16}=\dfrac{-64}{-16}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2\in D$