Question

Solve for x: 2 over 5 plus 3 over 5x equals x plus 5 over 10?

x = -3

x = 2

x = -3 and x = 2

No Solution

Answer 1

The equation is
\[(2/5)+(3/5x)=(x+5)/10\]
\[(2x+3)/(5x)=(x+5)/10\]
\[2x+3)/x=(x+5)/2\]
\[2(2x+3)=x(x+5)\]
\[4x+6=x^2+5x\]
\[x^2+x-6=0\]
Factorising
\[(x-2)(x+3)=0\]
Finally,
\[x=2\]
and
\[x=-3\]
The answer is x=2 and x=-3