Question

Solve

`(4 )/(4 - x) = (5)/((4 + x))`
for X

Answer 1

`Domain:\\4-x\\eq0\ \wedge\ 4+x\\eq0\\x\\eq4\ \wedge\ x\\eq-4\\\\(4)/(4-x)=(5)/(4+x)\qquad\text{cross multiply}\\\\4(4+x)=5(4-x)\qquad\text{use distributive property}\\\\(4)(4)+(4)(x)=(5)(4)+(5)(-x)\\\\16+4x=20-5x\qquad\text{subtract 16 from both sides}\\\\4x=4-5x\qquad\text{add 5x to both sides}\\\\9x=4\qquad\text{divide both sides by 9}\\\\\boxed{x=(4)/(9)}`