Find all values of x at which the tangent line to the given curve passes through the origin for y = 1/(x + 4)
The tangent is a line of slope "m".
The derivative of the function gives this slope.
As the tangent passes through the origin, it's equation is y=mx, as c=0.
Hence, the point of intersection of this tangent and the curve gives us x.
The equation of the tangent(s) through (0,0) is
Solving f(x) for the curve = mx for the line finds x.
Solving this, bearing in mind that x=-4 is not part of the domain of f(x) or f'(x) discovers x.
Hence multiply both fractions by (x+4) before solving for x.