Question

Solve for x 2/x+2 + 1/5 = 6/x+5

x = 0
x = –13
x = 13
x = 0 and x = 13

Answer 1

`(2)/(x+2)+(1)/(5)=(6)/(x+5)\qquad\text{multiply both sides by 5}\\\\(10)/(x+2)+1=(30)/(x+5)\\\\(10)/(x+2)+(x+2)/(x+2)=(30)/(x+5)\\\\(10+x+2)/(x+2)=(30)/(x+5)\\\\(x+12)/(x+2)=(30)/(x+5)\qquad\text{cross multiply}\\\\(x+12)(x+5)=30(x+2)\qquad\text{use distributive property}\\\\(x)(x)+(x)(5)+(12)(x)+(12)(5)=(30)(x)+(30)(2)\\\\x^2+5x+12x+60=30x+60\qquad\text{subtract 60 from both sides}\\\\x^2+17x=30x\qquad\text{subtract 30x from both sides}`

`x^2-13x=0\\\\x(x-13)=0\iff x=0\ \vee\ x-13=0\qquad\text{add 13 to both sides}\\\\\boxed{x=0\ \vee\ x=13}`