Question

Solve for x.
1/x + 1/x+16= 1/15

Answer 1

\[\frac{1}{x}+\frac{1}{x+16}=\frac{1}{15}\]


\[15(x+16)+15x=x(x+16)\]


\[15x+240+15x=x^2+16x\]


\[30x+240=x^2+16x\]


\[0=x^2+16x-30x-240\]


\[0=x^2-14x-240\]


\[x^2-14x-240=0\]


\[(x-24)(x+10)=0\]


\[x-24=0 \ \textrm{or} \ x+10=0\]


\[x=24 \ \textrm{or} \ x=-10\]

I'll leave the check to you.

Answer 2

Thanks Jim