Question

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

Answer 1

x = -2 or x = 2

Explanation:

`Domain:\\8+x\\eq0\ \wedge\ 8-x\\eq0\\\boxed{D:x\\eq-8\ \wedge\ x\\eq8}\\\\(60)/(8+x)+(60)/(8-x)=16\\\\(60(8-x))/((8+x)(8-x))+(60(8+x))/((8+x)(8-x))=16\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\(60(8-x)+60(8+x))/(8^2-x^2)=16\qquad\text{use the distributive property}\\\\((60)(8)+(60)(-x)+(60)(8)+(60)(x))/(64-x^2)=16\\\\(480-60x+480+60x)/(64-x^2)=16\qquad\text{combine like terms}\\\\((480+480)+(-60x+60x))/(64-x^2)=16\\\\(960)/(64-x^2)=16`

`(960)/(64-x^2)=(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)}\\\\(-16x^2)/(-16)=(-64)/(-16)\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2\in D`