+22 find all values of x such that \(\frac{2x}{x + 2} = -\frac{6}{x + 4}.\)
+499 Multiply both sides by (x+2) * (x+4) or "cross multiply" to get:
\(2x(x+4) = -6(x+2)\)
Expanding out, we get:
\(2x^2+8x = -6x - 12\)
Adding 6x and 12 on both sides of the equation, we then get the quadratic:
\(2x^2 +14x+12 = 0\)
We can then factor this into:
\((2x+2)(x+6) = 0\)
The values for which this is 0 are -1 and -6
