Question

Solve.

1/x - 1/x+4 = 1/3

Answer 1

are you still typing?

Answer 2

Is the 1/x+4 over both the x and 4 or just the x?

Answer 3

both its 1 over x+4

Answer 4

\[1/x-1/(x+4) = 1/3\]
Multiply both sides by x:
\[1-x/(x+4) = x/3\]
Write the left hand side as a single fraction:
\[4/(x+4) = x/3\]
Subtract x/3 from both sides:
\[4/(x+4)-x/3 = 0\]
Write the left hand side as a single fraction:
\[(-x^2-4 x+12)/(3 (x+4)) = 0\]
Multiply both sides by 3(x+4):
\[-x^2-4 x+12 = 0\]
Solve the quadratic equation by completing the square:
Divide both sides by -1:
\[x^2+4 x-12 = 0\]
Add 12 to both sides:
\[x^2+4 x = 12\]
Add 4 to both sides:
\[x^2+4 x+4 = 16\]
Factor the left hand side:
\[(x+2)^2 = 16\]
Take the square root of both sides:
\[|x+2| = 4\]
Eliminate the absolute value:
\[x+2 = -4 or x+2 = 4\]
Subtract 2 from both sides:
\[x = -6 or x+2 = 4\]
Subtract 2 from both sides:
\[x = -6 or x = 2\]